Method And Apparatus For Mitigation Of Outlier Noise

ABSTRACT

The present invention relates to nonlinear signal processing, and, in particular, to method and apparatus for mitigation of outlier noise in the process of analog-to-digital conversion. More generally, this invention relates to adaptive real-time signal conditioning, processing, analysis, quantification, comparison, and control, and to methods, processes and apparatus for real-time measuring and analysis of variables, including statistical analysis, and to generic measurement systems and processes which are not specially adapted for any specific variables, or to one particular environment. This invention also relates to methods and corresponding apparatus for mitigation of electromagnetic interference, and further relates to improving properties of electronic devices and to improving and/or enabling coexistence of a plurality of electronic devices. The invention further relates to post-processing analysis of measured variables and to post-processing statistical analysis.

CROSS REFERENCES TO RELATED APPLICATIONS

This application claims the benefit of the U.S. provisional patentapplications 62/444,828 (filed on 11 Jan. 2017) and 62/569,807 (filed on9 Oct. 2017).

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

None.

COPYRIGHT NOTIFICATION

Portions of this patent application contain materials that are subjectto copyright protection. The copyright owner has no objection to thefacsimile reproduction by anyone of the patent document or the patentdisclosure, as it appears in the Patent and Trademark Office patent fileor records, but otherwise reserves all copyright rights whatsoever.

TECHNICAL FIELD

The present invention relates to nonlinear signal processing, and, inparticular, to method and apparatus for mitigation of outlier noise inthe process of analog-to-digital conversion. More generally, thisinvention relates to adaptive real-time signal conditioning, processing,analysis, quantification, comparison, and control, and to methods,processes and apparatus for real-time measuring and analysis ofvariables, including statistical analysis, and to generic measurementsystems and processes which are not specially adapted for any specificvariables, or to one particular environment. This invention also relatesto methods and corresponding apparatus for mitigation of electromagneticinterference, and further relates to improving properties of electronicdevices and to improving and/or enabling coexistence of a plurality ofelectronic devices. The invention further relates to post-processinganalysis of measured variables and to post-processing statisticalanalysis.

BACKGROUND

Non-Gaussian (and, in particular, impulsive, or outlier) noise affectingcommunication and data acquisition systems may originate from amultitude of natural and technogenic (man-made) phenomena in a varietyof applications. Examples of natural impulsive (outlier) noise sourcesinclude ice cracking (in polar regions) and snapping shrimp (in warmerwaters) affecting underwater acoustics [1-3]. Electrical man-made noiseis transmitted into a system through the galvanic (direct electricalcontact), electrostatic coupling, electromagnetic induction, or RFwaves. Examples of systems and services harmfully affected bytechnogenic noise include various sensor, communication, and navigationdevices and services [4-15], wireless internet [16], coherent imagingsystems such as synthetic aperture radar [17], cable, DSL, and powerline communications [18-24], wireless sensor networks [25], and manyothers. An impulsive noise problem also arises when devices based on theultra-wideband (UWB) technology interfere with narrowband communicationsystems such as WLAN [26] or CDMA-based cellular systems [27]. Aparticular example of non-Gaussian interference is electromagneticinterference (EMI), which is a widely recognized cause of receptionproblems in communications and navigation devices. The detrimentaleffects of EMI are broadly acknowledged in the industry and includereduced signal quality to the point of reception failure, increased biterrors which degrade the system and result in lower data rates anddecreased reach, and the need to increase power output of thetransmitter, which increases its interference with nearby receivers andreduces the battery life of a device.

A major and rapidly growing source of EMI in communication andnavigation receivers is other transmitters that are relatively close infrequency and/or distance to the receivers. Multiple transmitters andreceivers are increasingly combined in single devices, which producesmutual interference. A typical example is a smartphone equipped withcellular, WiFi, Bluetooth, and GPS receivers, or a mobile WiFi hotspotcontaining an HSDPA and/or LTE receiver and a WiFi transmitter operatingconcurrently in close physical proximity. Other typical sources ofstrong EMI are on-board digital circuits, clocks, buses, and switchingpower supplies. This physical proximity, combined with a wide range ofpossible transmit and receive powers, creates a variety of challenginginterference scenarios. Existing empirical evidence [8, 28, 29] and itstheoretical support [6, 7, 10] show that such interference oftenmanifests itself as impulsive noise, which in some instances maydominate over the thermal noise [5, 8, 28].

A simplified explanation of non-Gaussian (and often impulsive) nature ofa technogenic noise produced by digital electronics and communicationsystems may be as follows. An idealized discrete-level (digital) signalmay be viewed as a linear combination of Heaviside unit step functions[30]. Since the derivative of the Heaviside unit step function is theDirac δ-function [31], the derivative of an idealized digital signal isa linear combination of Dirac δ-functions, which is a limitlesslyimpulsive signal with zero interquartile range and infinite peakedness.The derivative of a “real” (i.e. no longer idealized) digital signal maythus be viewed as a convolution of a linear combination of Diracδ-functions with a continuous kernel. If the kernel is sufficientlynarrow (for example, the bandwidth is sufficiently large), the resultingsignal would appear as an impulse train protruding from a continuousbackground signal. Thus impulsive interference occurs “naturally” indigital electronics as “di/dt” (inductive) noise or as the result ofcoupling (for example, capacitive) between various circuit componentsand traces, leading to the so-called “platform noise” [28]. Additionalillustrative mechanisms of impulsive interference in digitalcommunication systems may be found in [6-8, 10, 32].

The non-Gaussian noise described above affects the input (analog)signal. The current state-of-art approach to its mitigation is toconvert the analog signal to digital, then apply digital nonlinearfilters to remove this noise. There are two main problems with thisapproach. First, in the process of analog-to-digital conversion thesignal bandwidth is reduced (and/or the ADC is saturated), and aninitially impulsive broadband noise would appear less impulsive [7-10,32]. Thus its removal by digital filters may be much harder to achieve.While this can be partially overcome by increasing the ADC resolutionand the sampling rate (and thus the acquisition bandwidth) beforeapplying digital nonlinear filtering, this further exacerbates thememory and the DSP intensity of numerical algorithms, making themunsuitable for real-time implementation and treatment of non-stationarynoise. Thus, second, digital nonlinear filters may not be able to workin real time, as they are typically much more computationally intensivethan linear filters. A better approach would be to filter impulsivenoise from the analog input signal before the analog-to-digitalconverter (ADC), but such methodology is not widely known, even thoughthe concepts of rank filtering of continuous signals are well understood[32-37].

Further, common limitations of nonlinear filters in comparison withlinear filtering are that (1) nonlinear filters typically have variousdetrimental effects (e.g., instabilities and intermodulationdistortions), and (2) linear filters are generally better than nonlinearin mitigating broadband Gaussian (e.g. thermal) noise.

Time Domain Analysis of 1st- and 2nd-Order Delta-Sigma (ΔΣ) ADCs withLinear Analog Loop Filters

Nowadays, delta-sigma (ΔΣ) ADCs are used for converting analog signalsover a wide range of frequencies, from DC to several megahertz. Theseconverters comprise a highly oversampling modulator followed by adigital/decimation filter that together produce a high-resolutiondigital output. [38-40]. As discussed in this section, which reviews thebasic principle of operation of ΔΣ ADCs from a time domain prospective,a sample of the digital output of a ΔΣ ADC represents its continuous(analog) input by a weighted average over a discrete time interval (thatshould be smaller than the inverted Nyquist rate) around that sample.

Since frequency domain representation is of limited use in analysis ofnonlinear systems, let us first describe the basic ΔΣ ADCs with 1st- and2nd-order linear analog loop filters in the time domain. Such 1st- and2nd-order ΔΣ ADCs are illustrated in panels I and II of FIG. 1,respectively. Note that the vertical scales of the shown fragments ofthe signal traces vary for different fragments.

Without loss of generality, we may assume that if the input D to theflip-flop is greater than zero, D>0, at a specific instance in the clockcycle (e.g. the rising edge), then the output Q takes a negative valueQ=V_(c). If D<0 at a rising edge of the clock, then the output Q takes apositive value Q=V_(c). At other times, the output Q does not change. Wealso assume in this example that x(t) is effectively band-limited, andis bounded by V_(c) so that |x(t)|<V_(c) for all t. Further, the clockfrequency F_(s) is significantly higher (e.g. by more than about 2orders of magnitude) than the bandwidth B_(x) of x(t), log₁₀(F_(s)/B_(x))≳2. It may be then shown that, with the above assumptions,the input D to the flip-flop would be a zero-mean signal with an averagezero crossing rate much higher than the bandwidth of x(t).

Note that in the limit of infinitely large clock frequencyF_(s)(F_(s)→∞) the behavior of the flip-flop would be equivalent to thatof an analog comparator. Thus, while in practice a finite flip-flopclock frequency is used, based on the fact that it is orders ofmagnitude larger that the bandwidth of the signal of interest we may usecontinuous-time (e.g. (w*y)(t) and x(t−Δt)) rather than discrete-time(e.g. (w*y)[k] and x[k−m]) notations in reference to the ADC outputs, asa shorthand to simplify the mathematical description of our approach.

As can be seen in FIG. 1, for the 1st-order modulator shown in panel I

x(t)−y(t)=0,  (1)

and for the 2nd-order modulator shown in panel II

$\begin{matrix}{{\overset{\_}{\overset{.}{y}(t)} = {\frac{1}{\tau}\left\lbrack \overset{\_}{{x(t)} - {y(t)}} \right\rbrack}},} & (2)\end{matrix}$

where the overdot denotes a time derivative, and the overlines denoteaveraging over a time interval between any pair of threshold (includingzero) crossings of D (such as, e.g., the interval ΔT shown in FIG. 1).Indeed, for a continuous function ƒ(t), the time derivative of itsaverage over a time interval ΔT may be expressed as

$\begin{matrix}{{\overset{\_}{\overset{.}{f}(t)} = {\overset{.}{\overset{\_}{f(t)}} = {{\frac{d}{dt}\left\lbrack {\frac{1}{\Delta \; T}{\int_{t - {\Delta \; T}}^{t}{{ds}\mspace{14mu} {f(s)}}}} \right\rbrack} = {\frac{1}{\Delta \; T}\left\lbrack {{f(t)} - {f\left( {t - {\Delta \; T}} \right)}} \right\rbrack}}}},} & (3)\end{matrix}$

and it will be zero if ƒ(t)−ƒ(t−ΔT)=0.

Now, if the time averaging is performed by a lowpass filter with animpulse response w(t) and a bandwidth B_(w) much smaller than the clockfrequency, B_(w)<<F_(s), equation (1) implies that the filtered outputof the 1st-order ΔΣ ADC would be effectively equal to the filteredinput,

(w*y)(t)=(w*x)(t)+δy,  (4)

where the asterisk denotes convolution, and the term δy (the “ripple”,or “digitization noise”) is small and will further be neglected. Wewould assume from here on that the filter w(t) has a flat frequencyresponse and a constant group delay Δt over the bandwidth of x(t). Thenequation (4) may be rewritten as

(w*y)(t)=Z(t−Δt),  (5)

and the filtered output would accurately represent the input signal.

Since y(t) is a two-level staircase signal with a discrete step durationn/F_(s), where n is a natural (counting) number, it may be accuratelyrepresented by a 1-bit discrete sequence y[k] with the sampling rateF_(s). Thus the subsequent conversion to the discrete (digital) domainrepresentation of x(t) (including the convolution of y[k] with w[k] anddecimation to reduce the sampling rate) is rather straightforward andwill not be discussed further.

If the input to a 1st-order ΔΣ ADC consists of a signal of interest x(t)and an additive noise n(t), then the filtered output may be written as

(w*y)(t)=x(t−Δt)+(w*v)(t),  (6)

provided that |x(t−Δt)+(w*v)(t)|<V_(c) for all t. Since w(t) has a flatfrequency response over the bandwidth of x(t), it would not change thepower spectral density of the additive noise v(t) in the signalpassband, and the only improvement in the passband signal-to-noise ratiofor the output (w*y)(t) would come from the reduction of thequantization noise δy by a well designed filter w(t).

Similarly, equation (2) implies that the filtered output of the2nd-order ΔΣ ADC would be effectively equal to the filtered inputfurther filtered by a 1st order lowpass filter with the time constant τand the impulse response h_(τ)(t),

(w*y)(t)=(h _(τ) *w*x)(t).  (7)

From the differential equation for a 1st order lowpass filter it followsthat h_(τ)*(w+τ{dot over (w)})=w, and thus we may rewrite equation (7)as

(h _(τ)*(w+τ{dot over (w)})*y)(t)=(h _(τ) *w*x)(t).  (8)

Provided that τ is sufficiently small (e.g., τ≲1/(4πB_(x))), equation(8) may be further rewritten as

((w+τ{dot over (w)})*y)(t)=(w*x)(t)=x(t−Δt).  (9)

The effect of the 2nd-order loop filter on the quantization noise δy isoutside the scope of this disclosure and will not be discussed.

SUMMARY

Since at any given frequency a linear filter affects both the noise andthe signal of interest proportionally, when a linear filter is used tosuppress the interference outside of the passband of interest theresulting signal quality is affected only by the total power andspectral composition, but not by the type of the amplitude distributionof the interfering signal. Thus a linear filter cannot improve thepassband signal-to-noise ratio, regardless of the type of noise. On theother hand, a nonlinear filter has the ability to disproportionatelyaffect signals with different temporal and/or amplitude structures, andit may reduce the spectral density of non-Gaussian (e.g. impulsive)interferences in the signal passband without significantly affecting thesignal of interest. As a result, the signal quality may be improved inexcess of that achievable by a linear filter. Such non-Gaussian (and, inparticular, impulsive, or outlier, or transient) noise may originatefrom a multitude of natural and technogenic (man-made) phenomena. Thetechnogenic noise specifically is a ubiquitous and growing source ofharmful interference affecting communication and data acquisitionsystems, and such noise may dominate over the thermal noise. While thenon-Gaussian nature of technogenic noise provides an opportunity for itseffective mitigation by nonlinear filtering, current state-of-the-artapproaches employ such filtering in the digital domain, afteranalog-to-digital conversion. In the process of such conversion, thesignal bandwidth is reduced, and the broadband non-Gaussian noisebecomes more Gaussian-like. This substantially diminishes theeffectiveness of the subsequent noise removal techniques.

The present invention overcomes the limitations of the prior art throughincorporation of a particular type of nonlinear noise filtering of theanalog input signal into nonlinear analog filters preceding an ADC,and/or into loop filters of ΔΣ ADCs. Such ADCs thus combineanalog-to-digital conversion with analog nonlinear filtering, enablingmitigation of various types of in-band non-Gaussian noise andinterference, especially that of technogenic origin, including broadbandimpulsive interference. This may considerably increase quality of theacquired signal over that achievable by linear filtering in the presenceof such interference. An important property of the presented approach isthat, while being nonlinear in general, the proposed filters wouldlargely behave linearly. They would exhibit nonlinear behavior onlyintermittently, in response to noise outliers, thus avoiding thedetrimental effects, such as instabilities and intermodulationdistortions, often associated with nonlinear filtering.

The intermittently nonlinear filters of the present invention would alsoenable separation of signals (and/or signal components) withsufficiently different temporal and/or amplitude structures in the timedomain, even when these signals completely or partially overlap in thefrequency domain. In addition, such separation may be achieved withoutreducing the bandwidths of said signal components.

Even though the nonlinear filters of the present invention areconceptually analog filters, they may be easily implemented digitally,for example, in Field Programmable Gate Arrays (FPGAs) or software. Suchdigital implementations would require very little memory and would betypically inexpensive computationally, which would make them suitablefor real-time signal processing.

Further scope and the applicability of the invention will be clarifiedthrough the detailed description given hereinafter. It should beunderstood, however, that the specific examples, while indicatingpreferred embodiments of the invention, are presented for illustrationonly. Various changes and modifications within the spirit and scope ofthe invention should become apparent to those skilled in the art fromthis detailed description. Furthermore, all the mathematicalexpressions, diagrams, and the examples of hardware implementations areused only as a descriptive language to convey the inventive ideasclearly, and are not limitative of the claimed invention.

BRIEF DESCRIPTION OF FIGURES

FIG. 1. ΔΣ ADCs with 1st-order (I) and 2nd-order (II) linear loopfilters.

FIG. 2. Simplified diagram of improving receiver performance in thepresence of impulsive interference.

FIG. 3. Illustrative ABAINF block diagram.

FIG. 4. Illustrative examples of the transparency functions and theirrespective influence functions.

FIG. 5. Block diagrams of CMTFs with blanking ranges [α⁻, α₊] (a) andV⁻, V₊]/G (b).

FIG. 6. Resistance of CMTF to outlier noise. The cross-hatched timeintervals in panel (c) correspond to nonlinear CMTF behavior (zero rateof change).

FIG. 7. Illustration of differences in the error signal for the exampleof FIG. 6. The cross-hatched time intervals indicate nonlinear CMTFbehavior (zero rate of change).

FIG. 8. Simplified illustrated schematic of CMTF circuit implementation.

FIG. 9. Resistance of the CMTF circuit of FIG. 8 to outlier noise. Thecross-hatched time intervals in the lower panel correspond to nonlinearCMTF behavior.

FIG. 10. Using sums and/or differences of input and output of CMTF andits various intermediate signals for separating impulsive (outlier) andnon-impulsive signal components.

FIG. 11. Illustration of using CMTF with appropriate blanking range forseparating impulsive and non-impulsive (“background”) signal components.

FIG. 12. Illustrative block diagrams of an ADiC with time parameter Tand blanking range [α⁻, α₊].

FIG. 13. Simplified illustrative electronic circuit diagram of usingCMTF with appropriately chosen blanking range [α⁻, α₊] for separatingincoming signal x(t) into impulsive i(t) and non-impulsive s(t)(“background”) signal components.

FIG. 14. Illustration of separating incoming signal x(t) into impulsivei(t) and non-impulsive s(t) (“background”) components by the circuit ofFIG. 13.

FIG. 15. Illustration of separation of discrete input signal “x” intoimpulsive component “aux” and non-impulsive (“background”) component.“prime” using the MATLAB function of § 2.5 with appropriately chosenblanking values “alpha_p” and “alpha_m”.

FIG. 16. Illustrative block diagram of a circuit implementing equation(17) and thus tracking a qth quantile of y(t).

FIG. 17. Illustration of MTF convergence to steady state for differentinitial conditions.

FIG. 18. Illustration of QTFs' convergence to steady state for differentinitial conditions.

FIG. 19. Illustration of separation of discrete input signal “x” intoimpulsive component “aux” and non-impulsive (“background”) component“prime” using the MATLAB function of § 3.3 with the blanking rangecomputed as Tukey's range using digital QTFs.

FIG. 20. Illustrative block diagram of an adaptive intermittentlynonlinear filter for mitigation of outlier noise in the process ofanalog-to-digital conversion.

FIG. 21. Equivalent block diagram for the filter shown in FIG. 20operating in linear regime.

FIG. 22. Impulse and frequency responses of w[k] and w[k]+τw[k] used inthe subsequent examples.

FIG. 23. Comparison of simulated channel capacities for the linearprocessing chain (solid curves) and the CMTF-based chains with β=3(dotted and dashed curves). The dashed curves correspond to channelcapacities for the CMTF-based chain with added interference in anadjacent channel. The asterisks correspond to the noise and adjacentchannel interference conditions used in FIG. 24.

FIG. 24. Illustration of changes in the signal time- and frequencydomain properties, and in its amplitude distributions, while itpropagates through the signal processing chains, linear (points (a),(b), and (c) in panel II of FIG. 21), and the CMTF-based (points Ithrough IV, and point V, in FIG. 20).

FIG. 25. Alternative topology for signal processing chain shown in FIG.20.

FIG. 26. ΔΣ ADC with an CMTF-based loop filter.

FIG. 27. Modifying the amplitude density of the difference signal x−y bya 1st order lowpass filter.

FIG. 28. Impulse and frequency responses of w[k] and w[k]+(4πB_(x))⁻¹w[k] used in the examples of FIG. 29.

FIG. 29. Comparative performance of ΔΣ ADCs with linear and nonlinearanalog loop filters.

FIG. 30. Resistance of ΔΣ ADC with CMTF-based loop filter to increase inimpulsive noise.

FIG. 31. Outline of ΔΣ ADC with adaptive CMTF-based loop filter.

FIG. 32. Comparison of simulated channel capacities for the linearprocessing chain (solid lines) and the CMTF-based chains with β=1.5(dotted lines). The meaning of the asterisks is explained in the text.

FIG. 33A. Reduction of the spectral density of impulsive noise in thesignal baseband without affecting that of the signal of interest.

FIG. 33B. Reduction of the spectral density of impulsive noise in thesignal baseband without affecting that of the signal of interest.(Illustration similar to FIG. 33A with additional interference in anadjacent channel.)

FIG. 34. Illustrative signal chains for a ΔΣ ADC with linear loop anddecimation filters (panel (a)), and for a ΔΣ ADC with linear loop filterand ADiC-based digital filtering (panel (b)).

FIG. 35. Illustrative time-domain traces at points I through VI of FIG.34, and the output of the ΔΣ ADC with linear loop and decimation filtersfor the signal affected by AWGN only (w/o impulsive noise).

FIG. 36. Illustrative signal chains for a ΔΣ ADC with linear loop anddecimation filters (panel (a)), and for a ΔΣ ADC with linear loop filterand CMTF-based digital filtering (panel (b)).

FIG. 37. Illustrative time-domain traces at points I through VI of FIG.36, and the output of the ΔΣ ADC with linear loop and decimation filtersfor the signal affected by AWGN only (w/o impulsive noise).

FIG. 38. Illustrative signal chains for a ΔΣ ADC with linear loop anddecimation filters (panel (a)), and for a ΔΣ ADC with linear loop filterand ADiC-based digital filtering (panel (b)), with additional clippingof the analog input signal.

FIG. 39. Illustrative time-domain traces at points I through VI of FIG.38, and the output of the ΔΣ ADC with linear loop and decimation filtersfor the signal affected by AWGN only (w/o impulsive noise).

FIG. 40. Illustrative signal chains for a ΔΣ ADC with linear loop anddecimation filters (panel (a)), and for a ΔΣ ADC with linear loop filterand CMTF-based digital filtering (panel (b)), with additional clippingof the analog input signal.

FIG. 41. Illustrative time-domain traces at points I through VI of FIG.40, and the output of the ΔΣ ADC with linear loop and decimation filtersfor the signal affected by AWGN only (w/o impulsive noise).

FIG. 42. Analog (panel (a)) and digital (panel (b)) ABAINF deploymentfor mitigation of non-Gaussian (e.g. outlier) noise in the process ofanalog-to-digital conversion.

FIG. 43. Analog (panel (a)) and digital (panel (b)) ABAINF-based outlierfiltering in ΔΣ ADCs.

ABBREVIATIONS

ABAINF: Analog Blind Adaptive Intermittently Nonlinear Filter; A/D:Analog-to-Digital; ADC: Analog-to-Digital Converter (or Conversion);ADiC: Analog Differential Clipper; AFE: Analog Front End; AGC: AutomaticGain Control; ASIC: Application-Specific Integrated Circuit: ASSP:Application-Specific Standard Product; AWGN: Additive White GaussianNoise;

BAINF: Blind Adaptive Intermittently Nonlinear Filter; BER: Bit ErrorRate, or Bit. Error Ratio;

CDL: Canonical Differential Limiter: CDMA: Code Division MultipleAccess; CMTF: Clipped Mean Tracking Filter; COTS: CommercialOff-The-Shelf;

DSP: Digital Signal Processing/Processor;

EMC: electromagnetic compatibility; EMI: electromagnetic interference;

FIR: Finite Impulse Response; FPGA: Field Programmable Gate Array;

HSDPA: High Speed Downlink Packet. Access;

IC: Integrated Circuit; I/Q: In-phase/Quadrature; IQR: interquartilerange;

MAD: Mean/Median Absolute Deviation; MATLAB: MATrix LABoratory(numerical computing environment and fourth-generation programminglanguage developed by Math-Works); MTF: Median Tracking Filter;

NDL: Nonlinear Differential Limiter;

OOB: Out-Of-Band;

PDF: Probability Density Function; PSD: Power Spectral Density;

QTF: Quartile (or Quantile) Tracking Filter;

RF: Radio Frequency; RFI: Radio Frequency Interference; RMS: Root MeanSquare; RRC: Root Raised Cosine; RX: Receiver;

SNR: Signal-to-Noise Ratio;

UWB: Ultra-wideband;

VGA: Variable-Gain Amplifier;

1 Analog Intermittently Nonlinear Filters for Mitigation of OutlierNoise

In the simplified illustration that follows, our focus is not onproviding precise definitions and rigorous proof of the statements andassumptions, but on outlining the general idea of employingintermittently nonlinear filters for mitigation of outlier (e.g.impulsive) noise, and thus improving the performance of a communicationsreceiver in the presence of such noise.

1.1 Motivation and Simplified System Model

Let us assume that the input noise affecting a baseband signal ofinterest with unit power consists of two additive components: (i) aGaussian component with the power P_(G) in the signal passband, and (ii)an outlier (impulsive) component with the power P_(i) in the signalpassband. Thus if a linear antialiasing filter is used before theanalog-to-digital conversion (ADC), the resulting signal-to-noise ratio(SNR) may be expressed as (P_(G)+P_(i))⁻¹.

For simplicity, let us further assume that the outlier noise is whiteand consists of short (with the characteristic duration much smallerthan the reciprocal of the bandwidth of the signal of interest) randompulses with the average inter-arrival times significantly larger thantheir duration, yet significantly smaller than the reciprocal of thesignal bandwidth. When the bandwidth of such noise is reduced to withinthe baseband by linear filtering, its distribution would be wellapproximated by Gaussian [41]. Thus the observed noise in the basebandmay be considered Gaussian, and we may use the Shannon formula [42] tocalculate the channel capacity.

Let us now assume that we use a nonlinear antialiasing filter such thatit behaves linearly, and affects the signal and noise proportionally,when the baseband power of the impulsive noise is smaller than a certainfraction of that of the Gaussian component, P_(i)≤εP_(G) (ε≥0) resultingin the SNR (P_(G)+P_(i))⁻¹. However, when the baseband power of theimpulsive noise increases beyond εP_(G), this filter maintains itslinear behavior with respect to the signal and the Gaussian noisecomponent, while limiting the amplitude of the outlier noise in such away that the contribution of this noise into the baseband remainslimited to εP_(G)<P_(i). Then the resulting baseband SNR would be[(1+ε)P_(G)]⁻¹>(P_(G)+P_(i))⁻¹. We may view the observed noise in thebaseband as Gaussian, and use the Shannon formula to calculate the limiton the channel capacity.

As one may see from this example, by disproportionately affectinghigh-amplitude outlier noise while otherwise preserving linear behavior,such nonlinear antialiasing filter would provide resistance to impulsiveinterference, limiting the effects of the latter, for small e, to aninsignificant fraction of the Gaussian noise. FIG. 2 illustrates thiswith a simplified diagram of improving receiver performance in thepresence of impulsive interference by employing such analog nonlinearfilter before the ADC. In this illustration, ε=0.2.

2 Analog Blind Adaptive Intermittently Nonlinear Filters (ABAINFs) withthe Desired Behavior

The analog nonlinear filters with the behavior outlined in § 1.1 may beconstructed using the approach shown in FIG. 3, which provides anillustrative block diagram of an Analog Blind Adaptive IntermittentlyNonlinear Filter (ABAINF).

In FIG. 3, the influence function [43]

_(α−) ^(α+)(x) is represented as

_(α−) ^(α+)(x)=x

_(α−) ^(α+)(x), where

_(α−) ^(α+)(x) is a transparency function with the characteristictransparency range [α⁻, α₊]. We may require that

_(α−) ^(α+)+(x) is effectively (or approximately) unity for α⁻≤x≤α₊, andthat

_(α−) ^(α+) (|x|) decays to zero (e.g. monotonically) for x outside ofthe range [α⁻, α₊].

As one should be able to see in FIG. 3, a (nonlinear) differentialequation relating the input x(t) to the output x(t) of an ABAINF may bewritten as

$\begin{matrix}{{{\frac{d}{dt}\chi} = {{\frac{1}{\tau}{\mathcal{I}_{\alpha_{-}}^{\alpha_{+}}\left( {x - \chi} \right)}} = {\frac{x - \chi}{\tau}{_{\alpha_{-}}^{\alpha_{+}}\left( {x - \chi} \right)}}}},} & (10)\end{matrix}$

where τ is the ABAINF's time parameter (or time constant).

One skilled in the art will recognize that, according to equation (10),when the difference signal x(t)−χ(t) is within the transparency range[α⁻, α₊], the ABAINF would behave as a 1st order linear lowpass filterwith the 3 dB corner frequency 1/(2πτ), and, for a sufficiently largetransparency range, the ABAINF would exhibit nonlinear behavior onlyintermittently, when the difference signal extends outside thetransparency range.

If the transparency range [α⁻, α₊] is chosen in such a way that itexcludes outliers of the difference signal x(t)−χ(t), then, since thetransparency function

_(α−) ^(α+)(x) decays to zero for x outside of the range [α⁻, α₊], thecontribution of such outliers to the output χ(t) would be depreciated.

It may be important to note that outliers would be depreciateddifferentially, that is, based on the difference signal x(t)−χ(t) andnot the input signal x(t).

The degree of depreciation of outliers based on their magnitude woulddepend on how rapidly the transparency function

_(α−) ^(α+)(x) decays to zero for x outside of the transparency range.For example, as follows from equation (10), once the transparencyfunction decays to zero, the output χ(t) would maintain a constant valueuntil the difference signal x(t)−χ(t) returns to within non-zero valuesof the transparency function.

FIG. 4 provides several illustrative examples of the transparencyfunctions and their respective influence functions.

One skilled in the art will recognize that a transparency function withmultiple transparency ranges may also be constructed as a product of(e.g. cascaded) transparency functions, wherein each transparencyfunction is characterized by its respective transparency range.

2.1 A Particular ABAINF Example

As an example, let us consider a particular ABAINF with the influencefunction of a type shown in FIG. 4(iii), for a symmetrical transparencyrange [α⁻, α₊]=[−α, α]:

$\begin{matrix}{\mathcal{I}_{\alpha} = {{x\; {_{\alpha}(x)}} = {x \times \left\{ {\begin{matrix}1 & \left. {for}\mspace{14mu} \middle| x \middle| {\leq \alpha} \right. \\\frac{\mu\tau}{|x|} & {otherwise}\end{matrix},} \right.}}} & (11)\end{matrix}$

where α≥0 is the resolution parameter (with units “amplitude”),

≥0 is the time parameter (with units “time”), and μ≥0 is the rateparameter (with units “amplitude per time”).

For such an ABAINF, the relation between the input signal x(t) and thefiltered output signal χ(t) may be expressed as

$\begin{matrix}{{\overset{.}{\chi} = {\frac{x - \chi}{\tau}\left\lbrack {{\theta \left( \left. {\alpha -} \middle| {x - \chi} \right| \right)} + {\frac{\mu\tau}{\left| {x - \chi} \right|}{\theta \left( \left| {x - \chi} \middle| {- \alpha} \right. \right)}}} \right\rbrack}},} & (12)\end{matrix}$

where θ(x) is the Heaviside unit step function [30].

Note that when |x−χ|≤α (e.g., in the limit α→∞) equation (12) describesa 1st order analog linear lowpass filter (RC integrator) with the timeconstant τ (the 3 dB corner frequency 1/(2πτ)). When the magnitude ofthe difference signal |x−χ| exceeds the resolution parameter α, however,the rate of change of the output is limited to the rate parameter μ, andno longer depends on the magnitude of the incoming signal x(t),providing an output insensitive to outliers with a characteristicamplitude determined by the resolution parameter α. Note that for asufficiently large α this filter would exhibit nonlinear behavior onlyintermittently, in response to noise outliers, while otherwise acting asa 1st order linear lowpass filter.

Further note that for μ=α/τ equation (12) corresponds to the CanonicalDifferential Limiter (CDL) described in [9, 10, 24, 32], and in thelimit α→0 it corresponds to the Median Tracking Filter described in §3.1.

However, an important distinction of this ABAINF from the nonlinearfilters disclosed in [9, 10, 24, 32] would be that the resolution andthe rate parameters are independent from each other. This may providesignificant benefits in performance, ease of implementation, costreduction, and in other areas, including those clarified and illustratedfurther in this disclosure.

2.2 Clipped Mean Tracking Filter (CMTF)

The blanking influence function shown in FIG. 4(i) would be anotherparticular example of the ABAINF outlined in FIG. 3, where thetransparency function may be represented as a boxcar function,

_(α−) ^(α+)(x)=θ(x−α ⁻)−θ(x−α ₊).  (13)

For this particular choice, the ABAINF may be represented by thefollowing 1st order nonlinear differential equation:

$\begin{matrix}{{{\frac{d}{dt}\chi} = {\frac{1}{\tau}{\mathcal{B}_{\alpha_{-}}^{\alpha_{+}}\left( {x - \chi} \right)}}},} & (14)\end{matrix}$

where the blanking function β_(α−) ^(α+)(x) may be defined as

$\begin{matrix}{{\mathcal{B}_{\alpha_{-}}^{\alpha_{+}}(x)} = \left\{ {\begin{matrix}x & {{{for}\mspace{14mu} \alpha_{-}} \leq x \leq \alpha_{+}} \\0 & {otherwise}\end{matrix},} \right.} & (15)\end{matrix}$

and where [α⁻, α₊] may be called the blanking range.

We shall call an ABAINF with such influence function a 1st order ClippedMean Tracking Filter (CMTF).

A block diagram of a CMTF is shown in FIG. 5 (a). In this figure, theblanker implements the blanking function β_(α−) ^(α+)(x).

In a similar fashion, we may call a circuit implementing an influencefunction

_(α−) ^(α+)(x) a depreciator with characteristic depreciation (ortransparency, or influence) range [α⁻, α₊].

Note that, forb>0,

$\begin{matrix}{{{b^{- 1}{\mathcal{I}_{\alpha_{-}}^{\alpha_{+}}({bx})}} = {\mathcal{I}_{\frac{\alpha_{-}}{b}}^{\frac{\alpha_{+}}{b}}(x)}},} & (16)\end{matrix}$

and thus, if the blanker with the range [V⁻, V₊] is preceded by a gainstage with the gain G and followed by a gain stage with the gain G⁻¹,its apparent (or “equivalent”) blanking range would be [V⁻, V₊]/G, andwould no longer be hardware limited. Thus control of transparency rangesof practical ABAINF implementations may be performed by automatic gaincontrol (AGC) means. This may significantly simplify practicalimplementations of ABAINF circuits (e.g. by allowing constant hardwaresettings for the transparency ranges). This is illustrated in FIG. 5(b)for the CMTF circuit.

FIG. 6 illustrates resistance of a CMTF (with a symmetrical blankingrange [−α, α]) to outlier noise, in comparison with a 1st order linearlowpass filter with the same time constant (panel (a)), and with the CDLwith the resolution parameter α and τ₀=τ (panel (b)). The cross-hatchedtime intervals in the lower panel (panel (c)) correspond to nonlinearCMTF behavior (zero rate of change of the output). Note that theclipping (i.e. zero rate of change of the CMTF output) is performeddifferentially, based on the magnitude of the difference signalx(t)−χ(t) and not that of the input signal x(t).

We may call the difference between a filter output when the input signalis affected by impulsive noise and an “ideal” output (in the absence ofimpulsive noise) an “error signal”. Then the smaller the error signal,the better the impulsive noise suppression. FIG. 7 illustratesdifferences in the error signal for the example of FIG. 6. Thecross-hatched time intervals indicate nonlinear CMTF behavior (zero rateof change).

2.3 Illustrative CMTF Circuit

FIG. 8 provides a simplified illustration of implementing a CMTF bysolving equation (14) in an electronic circuit.

FIG. 9 provides an illustration of resistance of the CMTF circuit ofFIG. 8 to outlier noise. The cross-hatched time intervals in the lowerpanel correspond to nonlinear CMTF behavior.

While FIG. 8 illustrates implementation of a CMTF in an electroniccircuit comprising discrete components, one skilled in the art willrecognize that the intended electronic functionality may be implementedby discrete components mounted on a printed circuit board, or by acombination of integrated circuits, or by an application-specificintegrated circuit (ASIC). Further, one skilled in the art willrecognize that a variety of alternative circuit topologies may bedeveloped and/or used to implement the intended electronicfunctionality.

2.4 Using CMTFs for Separating Impulsive (Outlier) and Non-ImpulsiveSignal Components with Overlapping Frequency Spectra: AnalogDifferential Clippers (ADiCs)

In some applications it may be desirable to separate impulsive (outlier)and non-impulsive signal components with overlapping frequency spectrain time domain.

Examples of such applications would include radiation detectionapplications, and/or dual function systems (e.g. using radar as signalof opportunity for wireless communications and/or vice versa).

Such separation may be achieved by using sums and/or differences of theinput and the output of a CMTF and its various intermediate signals.This is illustrated in FIG. 10.

In this figure, the difference between the input to the CMTF integrator(signal τχ(t) at point III) and the CMTF output may be designated as aprime output of an Analog Differential Clipper (ADiC) and may beconsidered to be a non-impulsive (“background”) component extracted fromthe input signal. Further, the signal across the blanker (i.e. thedifference between the blanker input x(t)−χ(t) and the blanker outputτχ(t)) may be designated as an auxiliary output of an ADiC and may beconsidered to be an impulsive (outlier) component extracted from theinput signal.

FIG. 11 illustrates using a CMTF with an appropriately chosen blankingrange for separating impulsive and non-impulsive (“background”) signalcomponents. Note that the sum of the prime and the auxiliary ADiCoutputs would be effectively identical to the input signal, and thus theseparation of impulsive and non-impulsive components may be achievedwithout reducing signal's bandwidth.

FIG. 12 provides illustrative block diagrams of an ADiC with timeparameter τ and blanking range [α⁻, α₊].

FIG. 13 provides a simplified illustrative electronic circuit diagram ofusing a CMTF/ADiC with an appropriately chosen blanking range [a⁻, α₊]for separating incoming signal x(t) into impulsive i(t) andnon-impulsive s(t) (“background”) signal components, and FIG. 14provides an illustration of such separation by the circuit of FIG. 13.

2.5 Numerical Implementations of ABAINFs/CMTFs/ADiCs

Even though an ABAINF is an analog filter by definition, it may beeasily implemented digitally, for example, in a Field Programmable GateArray (FPGA) or software. A digital ABAINF would require very littlememory and would be typically inexpensive computationally, which wouldmake it suitable for real-time implementations.

An example of a numerical algorithm implementing a finite-differenceversion of a CMTF/ADiC may be given by the following MATLAB function:

function [chi,prime,aux] = CMTF_ADiC(x,t,tau,alpha_p,alpha_m)  chi =zeros(size(x));  aux = zeros(size(x));  prime = zeros(size(x));  dt =diff(t);  chi(1) = x(1);  B = 0;  for i = 2:length(x);   dX = x(i) −chi(i−1);   if dX>alpha_p(i−1)    B = 0;   elseif dX<alpha_m(i−1)    B =0;   else    B = dX;   end   chi(i) = chi(i−1) +B/(tau+dt(i−1))*dt(i−1); % numerical   antiderivative   prime(i) = B +chi(i−1);   aux(i) = dX − B;  end return

In this example, “x” is the input signal, “t” is the time array, “tau”is the CMTF's time constant. “alpha_p” and “alpha_m” are the upper andthe lower, respectively, blanking values, “chi” is the CMTF's output,“aux” is the extracted impulsive component (auxiliary ADiC output), and“prime” is the extracted non-impulsive (“background”) component (primeADiC output).

Note that we retain, for convenience, the abbreviations “ABAINF” and/or“ADiC” for finite-difference (digital) ABAINF and/or ADiCimplementations.

FIG. 15 provides an illustration of separation of a discrete inputsignal “x” into an impulsive component “aux” and a non-impulsive(“background”) component “prime” using the above MATLAB function withappropriately chosen blanking values “alpha_p” and “alpha_m”.

A digital signal processing apparatus performing an ABAINF filteringfunction transforming an input signal into an output filtered signalwould comprise an influence function characterized by a transparencyrange and operable to receive an influence function input and to producean influence function output, and an integrator function characterizedby an integration time constant and operable to receive an integratorinput and to produce an integrator output, wherein said integratoroutput is proportional to a numerical antiderivative of said integratorinput.

A hardware implementation of a digital ABAINF/CMTF/ADiC filteringfunction may be achieved by various means including, but not limited to,general-purpose and specialized microprocessors (DSPs),microcontrollers, FPGAs, ASICs, and ASSPs. A digital or a mixed-signalprocessing unit performing such a filtering function may also perform avariety of other similar and/or different functions.

3 Quantile Tracking Filters as Robust Means to Establish the ABAINFTransparency Range(s)

Let y(t) be a quasi-stationary bandpass (zero-mean) signal with a finiteinterquartile range (IQR), characterised by an average crossing rate

ƒ

of the threshold equal to some quantile q, 0<q<1, of y(t). (See [33, 34]for discussion of quantiles of continuous signals, and [44, 45] fordiscussion of threshold crossing rates.) Let us further consider thesignal Q_(q)(t) related to y(t) by the following differential equation:

$\begin{matrix}{{{\frac{d}{dt}Q_{q}} = {\frac{A}{T}\mspace{14mu}\left\lbrack {{{sgn}\left( {y - Q_{q}} \right)} + {2q} - 1} \right\rbrack}},} & (17)\end{matrix}$

where A is a constant (with the same units as y and Q_(q)), and T is aconstant with the units of time. According to equation (17), Q_(q)(t) isa piecewise-linear signal consisting of alternating segments withpositive (2qA/T) and negative (2(q−1)A/T) slopes. Note thatQ_(q)(t)≈const for a sufficiently small A/T (e.g., much smaller than theproduct of the IQR and the average crossing rate

ƒ

of y(t) and its qth quantile), and a steady-state solution of equation(17) can be written implicitly as

θ(Q _(q) −y)≈q,  (18)

where θ(x) is the Heaviside unit step function [30] and the overlinedenotes averaging over some time interval ΔT>>

ƒ

. Thus Q_(q) would approximate the qth quantile of y(t) [33, 34] in thetime interval ΔT.

We may call an apparatus (e.g. an electronic circuit) effectivelyimplementing equation (17) a Quantile Tracking Filler.

Despite its simplicity, a circuit implementing equation (17) may providerobust means to establish the ABAINF transparency range(s) as a linearcombination of various quantiles of the difference signal (e.g. its 1stand 3rd quartiles and/or the median). We will call such a circuit forq=½ a Median Tracking Filter (MTF), and for q=¼ and/or q=¾ a QuartileTracking Filter (QTF).

FIG. 16 provides an illustrative block diagram of a circuit implementingequation (17) and thus tracking a qth quantile of y(t). As one may seein the figure, the difference between the input y(t) and the quantileoutput Q_(q)(t) forms the input to an analog comparator which implementsthe function A sgn(y(t)−Q_(q)(t)). In reference to FIG. 16, we may callthe term (2q−1) A added to the integrator input as the “quantile settingsignal”. A sum of the comparator output and the quantile setting signalforms the input of an integrator characterized by the time constant T,and the output of the integrator forms the quantile output Q_(q)(t).

3.1 Median Tracking Filter

Let x(t) be a quasi-stationary signal characterized by an averagecrossing rate

ƒ

of the threshold equal to the second quartile (median) of x(t). Let usfurther consider the signal Q₂(t) related to x(t) by the followingdifferential equation:

$\begin{matrix}{{{\frac{d}{dt}Q_{2}} = {\frac{A}{T}{{sgn}\left( {x - Q_{2}} \right)}}},} & (19)\end{matrix}$

where A is a constant with the same units as x and Q₂, and T is aconstant with the units of time. According to equation (19). Q₂(t) is apiecewise-linear signal consisting of alternating segments with positive(A/T) and negative (−A/T) slopes. Note that Q₂(t)≈const for asufficiently small A/T (e.g., much smaller than the product of theinterquartile range and the average crossing rate

ƒ

of x(t) and its second quartile), and a steady-state solution ofequation (19) may be written implicitly as

θ(Q ₂ −x)≈½,  (20)

where the overline denotes averaging over some time interval ΔT>><ƒ>⁻¹.Thus Q₂ approximates the second quartile of x(t) in the time intervalΔT, and equation (19) describes a Median Tracking Filter (MTF). FIG. 17illustrates the MTF's convergence to the steady state for differentinitial conditions.

3.2 Quartile Tracking Filters

Let y(t) be a quasi-stationary bandpass (zero-mean) signal with a finiteinterquartile range (IQR), characterised by an average crossing rate <ƒ>of the threshold equal to the third quartile of y(t). Let us furtherconsider the signal Q₃(t) related to y(t) by the following differentialequation:

$\begin{matrix}{{{\frac{d}{dt}Q_{3}} = {\frac{A}{T}\left\lbrack {{{sgn}\left( {y - Q_{3}} \right)} + \frac{1}{2}} \right\rbrack}},} & (21)\end{matrix}$

where A is a constant (with the same units as y and Q₃), and T is aconstant with the units of time. According to equation (21), Q₃(t) is apiecewise-linear signal consisting of alternating segments with positive(3A/(2T)) and negative (−A/(2T)) slopes. Note that Q₃(t)≈const for asufficiently small A/T (e.g., much smaller than the product of the IQRand the average crossing rate <ƒ> of y(t) and its third quartile), and asteady-state solution of equation (21) may be written implicitly as

θ(Q ₃ −y)≈¾,  (22)

where the overline denotes averaging over some time interval ΔT><ƒ>⁻¹.Thus Q₃ approximates the third quartile of y(t) [33, 34] in the timeinterval ΔT.

Similarly, for

$\begin{matrix}{{\frac{d}{dt}Q_{1}} = {\frac{A}{T}\left\lbrack {{{sgn}\left( {y - Q_{1}} \right)} - \frac{1}{2}} \right\rbrack}} & (23)\end{matrix}$

a steady-state solution may be written as

θ(Q ₂ −y)≈¼,  (24)

and thus Q₁ would approximate the first quartile of y(t) in the timeinterval ΔT.

FIG. 18 illustrates the QTFs' convergence to the steady state fordifferent initial conditions.

One skilled in the art will recognize that (1) similar tracking filtersmay be constructed for other quantiles (such as, for example, terciles,quintiles, sextiles, and so on), and (2) a robust range [α⁻, α₊] thatexcludes outliers may be constructed in various ways, as, for example, alinear combination of various quantiles.

3.3 Numerical Implementations of ABAINFs/CMTFs/ADiCs Using QuantileTracking Filters as Robust Means to Establish the Transparency Range

For example, an ABAINF/CMTF/ADiC with an adaptive (possibly asymmetric)transparency range [α⁻, α₊] may be designed as follows. To ensure thatthe values of the difference signal x(t)−χ(t) that lie outside of [α⁻,α₊] are outliers, one may identify [α⁻, α₊] with Tukey's range [46], alinear combination of the 1st (Q₁) and the 3rd (Q₃) quartiles of thedifference signal:

[α⁻,α₊ ]=[Q ₁−β(Q ₃ −Q ₁),Q ₃+β(Q ₃ −Q ₁)].  (25)

where β is a coefficient of order unity (e.g. β=1.5).

An example of a numerical algorithm implementing a finite-differenceversion of a CMTF/ADiC with the blanking range computed as Tukey's rangeof the difference signal using digital QTFs may be given by the MATLABfunction “CMTF_ADiC_alpha” below.

In this example, the CMTF/ADiC filtering function further comprises ameans of tracking the range of the difference signal that effectivelyexcludes outliers of the difference signal, and wherein said meanscomprises a QTF estimating a quartile of the difference signal:

function [chi,prime,aux,alpha_p,alpha_m] =CMTF_ADiC_alpha(x,t,tau,beta,mu)  chi = zeros(size(x));  aux =zeros(size(x));  prime = zeros(size(x));  alpha_p = zeros(size(x)); alpha_m = zeros(size(x));  dt = diff(t);  chi(1) = x(1);  Q1 = x(1); Q3 = x(1);  B = 0;  for i = 2:length(x);   dX = x(i) − chi(i−1); %-------------------------------------------------------------------- % Update 1st and 3rd quartile values:   Q1 = Q1 +mu*(sign(dX−Q1)−0.5)*dt(i−1); % numerical   antiderivative   Q3 = Q3 +mu*(sign(dX−Q3)+0.5)*dt(i−1); % numerical   antiderivative %-------------------------------------------------------------------- % Calculate blanking range:   alpha_p(i) = Q3 + beta*(Q3−Q1);  alpha_m(i) = Q1 − beta*(Q3−Q1); %--------------------------------------------------------------------  if dX>alpha_p(i)    B = 0;   elseif dX<alpha_m(i)    B = 0;   else   B = dX;   end   chi(i) = chi(i−1) + B/(tau+dt(i−1))*dt(i−1); %numerical   antiderivative   prime(i) = B + chi(i−1);   aux(i) = dX − B; end return

FIG. 19 provides an illustration of separation of discrete input signal“x” into impulsive component “aux” and non-impulsive (“background”)component “prime” using the above MATLAB function of § 3.3 with theblanking range computed as Tukey's range using digital QTFs. The upperand lower limits of the blanking range are shown by the dashed lines inpanel (b).

3.4 Adaptive Influence Function Design

The influence function choice determines the structure of the localnonlinearity imposed on the input signal. If the distribution of thenon-Gaussian technogenic noise is known, then one may invoke the classiclocally most powerful (LMP) test [47] to detect and mitigate the noise.The LMP test involves the use of local nonlinearity whose optimal choicecorresponds to

${{g_{l_{o}}(n)} = {- \frac{f^{\prime}(n)}{f(n)}}},$

where ƒ(n) represents the technogenic noise density function and ƒ′(n)is its derivative. While the LMP test and the local nonlinearity istypically applied in the discrete time domain, the present inventionenables the use of this idea to guide the design of influence functionsin the analog domain. Additionally, non-stationarity in the noisedistribution may motivate an online adaptive strategy to designinfluence functions.

Such adaptive online influence function design strategy may explore themethodology disclosed herein. In order to estimate the influencefunction, one may need to estimate both the density and its derivativeof the noise. Since the difference signal x(t)−χ(t) of an ABAINF wouldeffectively represent the non-Gaussian noise affecting the signal ofinterest, one may use a bank of N quantile tracking filters described in§ 3 to determine the sample quantiles (Q₁, Q₂, . . . , Q_(N)) of thedifference signal. Then one may use a non-parametric regressiontechnique such as, for example, a local polynomial kernel regressionstrategy to simultaneously estimate (1) the time-dependent amplitudedistribution function Φ(D, t) of the difference signal, (2) its densityfunction ϕ(D, t), and (3) the derivative of the density function ∂ϕ(D,t)/∂D.

4 Adaptive Intermittently Nonlinear Analog Filters for Mitigation ofOutlier Noise in the Process of Analog-to-Digital Conversion

Let us now illustrate analog-domain mitigation of outlier noise in theprocess of analog-to-digital (A/D) conversion that may be performed bydeploying an ABAINF (for example, a CMTF) ahead of an ADC.

An illustrative principal block diagram of an adaptive CMTF formitigation of outlier noise disclosed herein is shown in FIG. 20.Without loss of generality, here it may be assumed that the outputranges of the active components (e.g. the active filters, integrators,and comparators), as well as the input range of the analog-to-digitalconverter (A/D), are limited to a certain finite range, e.g., to thepower supply range ±V_(c).

The time constant τ may be such that 1/(2ττ) is similar to the cornerfrequency of the anti-aliasing filter (e.g., approximately twice thebandwidth of the signal of interest B_(x)), and the time constant Tshould be two to three orders of magnitude larger than B_(x) ⁻¹. Thepurpose of the front-end lowpass filter would be to sufficiently limitthe input noise power. However, its bandwidth may remain sufficientlywide (i.e. γ>>1) so that the impulsive noise is not excessivelybroadened.

Without loss of generality, we may further assume that the gain K isconstant (and is largely determined by the value of the parameter γ,e.g., as K˜√{square root over (γ)}), and the gains G and g are adjusted(e.g. using automatic gain control) in order to well utilize theavailable output ranges of the active components, and the input range ofthe A/D. For example, G and g may be chosen to ensure that the averageabsolute value of the output signal (i.e., observed at point IV) isapproximately V_(c)/5, and the average value of Q*₂(t) is approximatelyconstant and is smaller than V_(c).

4.1 CMTF Block

For the Clipped Mean Tracking Filter (CMTF) block shown in FIG. 20, theinput x(t) and the output χ(t) signals may be related by the following1st order nonlinear differential equation:

$\begin{matrix}{{{\frac{d}{dt}\chi} = {\frac{1}{\tau}{\mathcal{B}_{\frac{V_{c}}{g}}\left( {x - \chi} \right)}}},} & (26)\end{matrix}$

where the symmetrical blanking function β_(α)(x) may be defined as

$\begin{matrix}{{\mathcal{B}_{\alpha}(x)} = \left\{ {\begin{matrix}x & \left. {for}\mspace{14mu} \middle| x \middle| {\leq \alpha} \right. \\0 & {{otherwise}\mspace{34mu}}\end{matrix},} \right.} & (27)\end{matrix}$

and where the parameter α is the blanking value.

Note that for the blanking values such that |x(t)−χ(t)|≤V_(c)/g for allt, equation (26) describes a 1st order linear lowpass filter with thecorner frequency 1/(2ττ), and the filter shown in FIG. 20 operates in alinear regime (see FIG. 21). However, when the values of the differencesignal x(t)−χ(t) are outside of the interval [−V_(c)/g, V_(c)/g], therate of change of χ(t) is zero and no longer depends on the magnitude ofx(t)−χ(t). Thus, if the values of the difference signal that lie outsideof the interval [−V_(c)/g, V_(c)/g] are outliers, the output, χ(t) wouldbe insensitive to further increase in the amplitude of such outliers.FIG. 6 illustrates resistance of a CMTF to outlier noise, in comparisonwith a 1st order linear lowpass filter with the same time constant. Theshaded time intervals correspond to nonlinear CMTF behavior (zero rateof change). Note that the clipping (i.e. zero rate of change of the CMTFoutput) is performed differentially, based on the magnitude of thedifference signal |x−χ| and not that of the input signal x.

In the filter shown in FIG. 20 the range [−V_(c)/g, V_(c)/g] thatexcludes outliers is obtained as Tukey's range [46] for a symmetricaldistribution, with V_(c)/g given by

$\begin{matrix}{{\frac{{VB}_{c}}{g} = {\left( {1 + {2\beta}} \right)Q_{2}^{*}}},} & (28)\end{matrix}$

where Q*₂ is the 2nd quartile (median) of the absolute value of thedifference signal |x(t)−χ(t)|, and where β is a coefficient of orderunity (e.g. β=3). While in this example we use Tukey's range, variousalternative approaches to establishing a robust interval [−V_(c)/g,V_(c)/g] may be employed.

In FIG. 20, the MTF circuit receiving the absolute value of the blankerinput and producing the MTF output, together with a means to maintainsaid MTF output at approximately constant value (e.g. using automaticgain control) and the gain stages preceding and following the blanker,establish a blanking range that effectively excludes outliers of theblanker input.

It would be important to note that, as illustrated in panel I of FIG.21, in the linear regime the CMTF would operate as a 1st order linearlowpass filter with the corner frequency 1/(2ττ). It would exhibitnonlinear behavior only intermittently, in response to outliers in thedifference signal, thus avoiding the detrimental effects, such asinstabilities and intermodulation distortions, often associated withnonlinear filtering.

4.2 Baseband Filter

In the absence of the CMTF in the signal processing chain, the basebandfilter following the A/D would have the impulse response w[k] that maybe viewed as a digitally sampled continuous-time impulse response w(t)(see panel II of FIG. 21). As one may see in FIG. 20, the impulseresponse of this filter may be modified by adding the term τ{dot over(w)}[k], where the dot over the variable denotes its time derivative,and where {dot over (w)}[k] may be viewed as a digitally sampledcontinuous-time function {dot over (w)}(t). This added term wouldcompensate for the insertion of a 1st order linear lowpass filter in thesignal chain, as illustrated in FIG. 21.

Indeed, from the differential equation for a 1st order lowpass filter itwould follow that h_(τ)*(w+τ{dot over (w)})=w, where the asteriskdenotes convolution and where h_(τ)(t) is the impulse response of the1st order linear lowpass filter with the corner frequency 1/(2πτ). Thus,provided that τ is sufficiently small (e.g., T≲1/(2πB_(aa)), whereB_(aa) is the nominal bandwidth of the anti-aliasing filter), the signalchains shown in panels I and II of FIG. 21 would be effectivelyequivalent. The impulse and frequency responses of w[k] (aroot-raised-cosine filter with the roll-off factor ¼, bandwidth5B_(x)/4, and the sampling rate 8B_(x)) and w[k]+τ{dot over (w)}[k](withτ=1/(4πB_(x))) used in the subsequent examples of this section are shownin FIG. 22.

4.3 Comparative Performance Examples 4.3.1 Simulation Parameters

To emulate the analog signals in the simulated examples presented below,the digitisation rate was chosen to be significantly higher (by abouttwo orders of magnitude) than the A/D sampling rate.

The signal of interest is a Gaussian baseband signal in the nominalfrequency rage [0, B_(x)]. It is generated as a broadband white Gaussiannoise filtered with a root-raised-cosine filter with the roll-off factor¼ and the bandwidth 5B_(x)/4.

The noise affecting the signal of interest is a sum of an Additive WhiteGaussian Noise (AWGN) background component and white impulsive noisei(t). In order to demonstrate the applicability of the proposed approachto establishing a robust interval [−V_(c)/g, V_(c)/g] for asymmetricaldistributions, the impulsive noise is modelled as asymmetrical(unipolar) Poisson shot noise:

$\begin{matrix}{{{i(t)} = \left| {v(t)} \middle| {\sum\limits_{k = 1}^{\infty}\; {\delta \left( {t - t_{k}} \right)}} \right.},} & (29)\end{matrix}$

where v(t) is AWGN noise, t_(k) is the k-th arrival time of a Poissonpoint process with the rate parameter λ, and δ(x) is the Diracδ-function [31]. In the examples below, λ=2B_(x).

The A/D sampling rate is 8B_(x) (that assumes a factor of 4 oversamplingof the signal of interest), the A/D resolution is 12 bits, and theanti-aliasing filter is a 2nd order Butterworth lowpass filter with thecorner frequency 2B_(x). Further, the range of the comparators in theQTFs is ±A=±V_(c), the time constants of the integrators are7=1/(4πB_(x)) and T=100/B_(x). The impulse responses of the basebandfilters w[k] and w[k]+τ{dot over (w)}[k] are shown in the upper panel ofFIG. 22.

The front-end lowpass filter is a 2nd order Bessel with the cutofffrequency γ/(2πτ). The value of the parameter γ is chosen as γ=16, andthe gain of the anti-aliasing filter is K=√{square root over (γ)}=4. Thegains G and g are chosen to ensure that the average absolute value ofthe output signal (i.e., observed at point IV in FIG. 20 and at point(c) in FIG. 21) is approximately V_(c)/5, and

${{Q_{2}^{*}(t)} \approx \frac{V_{c}}{1 + {2\beta}}} = {{const}.}$

4.3.2 Comparative Channel Capacities

For the simulation parameters described above, FIG. 23 compares thesimulated channel capacities (calculated from the baseband SNRs usingthe Shannon formula [42]) for various signal+noise compositions, for thelinear signal processing chain shown in panel II of FIG. 21 (solidcurves) and the CMTF-based chain of FIG. 20 with 3=3 (dotted curves).

As one may see in FIG. 23 (and compare with the simplified diagram ofFIG. 2), for a sufficiently large β both linear and the CMTF-basedchains provide effectively equivalent performance when the AWGNdominates over the impulsive noise. However, the CMTF-based chains areinsensitive to further increase in the impulsive noise when the latterbecomes comparable or dominates over the thermal (Gaussian) noise, thusproviding resistance to impulsive interference.

Further, the dashed curves in FIG. 23 show the simulated channelcapacities for the CMTF-based chain of FIG. 20 (with β=3) whenadditional interference in an adjacent channel is added, as would be areasonably common practical scenario. The passband of this interferenceis approximately [3B_(x), 4B_(x)], and the total power is approximately4 times (6 dB) larger that that of the signal of interest. As one maysee in FIG. 23, such interference increases the apparent blanking valueneeded to maintain effectively linear CMTF behaviour in the absence ofthe outliers, reducing the effectiveness of the impulsive noisesuppression (more noticeably for higher AWGN SNRs).

It may be instructive to illustrate and compare the changes in thesignal's time and frequency domain properties, and in its amplitudedistributions, while it propagates through the signal processing chains,linear (points (a), (b), and (c) in panel II of FIG. 21), and theCMTF-based (points I through IV, and point V, in FIG. 20). Such anillustration is provided in FIG. 24. In the figure, the dashed lines(and the respective cross-hatched areas) correspond to the “ideal”signal of interest (without noise and adjacent channel interference),and the solid lines correspond to the signal+noise+interferencemixtures. The leftmost panels show the time domain traces, the rightmostpanels show the power spectral densities (PSDs), and the middle panelsshow the amplitude densities. The baseband power of the AWGN is onetenth of that of the signal of interest (10 dB AWGN SNR), and thebaseband power of the impulsive noise is approximately 8 times (9 dB)that of the AWGN. The value of the parameter β for Tukey's range is β=3.(These noise and adjacent channel interference conditions, and the valueβ=3, correspond to the respective channel capacities marked by theasterisks in FIG. 23).

Measure of Peakedness—

In the panels showing the amplitude densities, the peakedness of thesignal+noise mixtures is measured and indicated in units of “decibelsrelative to Gaussian” (dBG). This measure is based on the classicaldefinition of kurtosis [48], and for a real-valued signal may beexpressed in terms of its kurtosis in relation to the kurtosis of theGaussian (aka normal) distribution as follows [9, 10]:

$\begin{matrix}{{{K_{dBG}(x)} = {10{\lg \left\lbrack \frac{\langle\left( {x - {\langle x\rangle}} \right)^{4}\rangle}{3{\langle\left( {x - {\langle x\rangle}} \right)^{2}\rangle}^{2}} \right\rbrack}}},} & (30)\end{matrix}$

where the angular brackets denote the time averaging. According to thisdefinition, a Gaussian distribution would have zero dBG peakedness,while sub-Gaussian and super-Gaussian distributions would have negativeand positive dBG peakedness, respectively. In terms of the amplitudedistribution of a signal, a higher peakedness compared to a Gaussiandistribution (super-Gaussian) normally translates into “heavier tails”than those of a Gaussian distribution. In the time domain, highpeakedness implies more frequent occurrence of outliers, that is, animpulsive signal.

Incoming Signal—

As one may see in the upper row of panels in FIG. 24, the incomingimpulsive noise dominates over the AWGN. The peakedness of thesignal+noise mixture is high (14.9 dBG), and its amplitude distributionhas a heavy “tail” at positive amplitudes.

Linear Chain—

The anti-aliasing filter in the linear chain (row (b)) suppresses thehigh-frequency content of the noise, reducing the peakedness to 2.3 dBG.The matching filter in the baseband (row (c)) further limits the noisefrequencies to within the baseband, reducing the peakedness to 0 dBG.Thus the observed baseband noise may be considered to be effectivelyGaussian, and we may use the Shannon formula [42] based on the achievedbaseband SNR (0.9 dB) to calculate the channel capacity. This is markedby the asterisk on the respective solid curve in FIG. 23. (Note that theachieved 0.9 dB baseband SNR is slightly larger than the “ideal” 0.5 dBSNR that would have been observed without “clipping” the outliers of theoutput of the anti-aliasing filter by the A/D at +±1.)

CMTF-Based Chain—

As one may see in the panels of row V, the difference signal largelyreflects the temporal and the amplitude structures of the noise and theadjacent channel signal. Thus its output may be used to obtain the rangefor identifying the noise outliers (i.e. the blanking value V_(c)/g).Note that a slight increase in the peakedness (from 14.9 dBG to 15.4dBG) is mainly due to decreasing the contribution of the Gaussian signalof interest, as follows from the linearity property of kurtosis.

As may be seen in the panels of row II, since the CMTFdisproportionately affects signals with different temporal and/oramplitude structures, it reduces the spectral density of the impulsiveinterference in the signal passband without significantly affecting thesignal of interest. The impulsive noise is notably decreased, while theamplitude distribution of the filtered signal+noise mixture becomeseffectively Gaussian.

The anti-aliasing (row III) and the baseband (row IV) filters furtherreduce the remaining noise to within the baseband, while the modifiedbaseband filter also compensates for the insertion of the CMTF in thesignal chain. This results in the 9.3 dB baseband SNR, leading to thechannel capacity marked by the asterisk on the respective dashed-linecurve in FIG. 23.

4.4 Alternative Topology for Signal Processing Chain Shown in FIG. 20

FIG. 25 provides an illustration of an alternative topology for signalprocessing chain shown in FIG. 20, where the blanking range isdetermined according to equation (36).

One skilled in the art will recognize that the topology shown in FIG. 20and the topology shown in FIG. 25 both comprise a CMTF filter(transforming an input signal x(t) into an output signal χ(t))characterized by a blanking range, and a robust means to establish saidblanking range in such a way that it excludes the outliers in thedifference signal x(t)−χ(t).

In FIG. 25, two QTFs receive a signal proportional to the blanker inputand produce two QTF outputs, corresponding to the 1st and the 3rdquartiles of the QTF input. Then the blanking range of the blanker isestablished as a linear combination of these two outputs.

5 ΔΣ ADC with CMTF-Based Loop Filter

While § 4 discloses mitigation of outlier noise in the process ofanalog-to-digital conversion by ADiCs/CMTFs deployed ahead of an ADC,CMTF-based outlier noise filtering of the analog input signal may alsobe incorporated into loop filters of ΔΣ analog-to-digital converters.

Let us consider the modifications to a 2nd-order ΔΣ ADC depicted in FIG.26. (Note that the vertical scales of the shown fragments of the signaltraces vary for different, fragments.) We may assume from here on thatthe 1st order lowpass filters with the time constant τ and the impulseresponse h_(τ)(t) shown in the figure have a bandwidth (as signified bythe 3 dB corner frequency) that is much larger than the bandwidth of thesignal of interest B_(x), yet much smaller than the sampling (clock)frequency F_(s). For example, the bandwidth of h_(τ)(t) may beapproximately equal to the geometric mean of B_(x) and F_(s), resultingin the following value for τ:

$\begin{matrix}{\tau \approx {\frac{1}{2\pi \sqrt{B_{x}F_{s}}}.}} & (31)\end{matrix}$

As one may see in FIG. 26, the first integrator (with the time constantγτ) is preceded by a (symmetrical) blanker, where the (symmetrical)blanking function B_(α)(x) may be defined as

$\begin{matrix}{{\mathcal{B}_{\alpha}(x)} = \left\{ {\begin{matrix}x & \left. {for}\mspace{14mu} \middle| x \middle| {\leq \alpha} \right. \\0 & {otherwise}\end{matrix},} \right.} & (32)\end{matrix}$

and where α is the blanking value.

As shown in the figure, the input x(t) and the output y(t) may berelated by

$\begin{matrix}{{{\frac{d}{dt}\overset{\_}{h_{\tau}*y}} = {\frac{1}{\gamma\tau}\overset{\_}{\mathcal{B}_{\alpha}\left( {h_{\tau}*\left( {x - y} \right)} \right)}}},} & (33)\end{matrix}$

where the overlines denote averaging over a time interval between anypair of threshold (including zero) crossings of D (such as, e.g., theinterval ΔT shown in FIG. 26), and the filter represented by equation(33) may be referred to as a Clipped Mean Tracking Filler (CMTF). Notethat without the time averaging equation (33) corresponds to the ABAINFdescribed by equation (12) with μ=0, where x and χ replaced by h_(τ)*xand h_(τ)*y, respectively.

The utility of the 1st order lowpass filters h_(τ)(t) would be, first,to modify the amplitude density of the difference signal x−y so that fora slowly varying signal of interest x(t) the mean and the median valuesof h_(τ)*(x−y) in the time interval ΔT would become effectivelyequivalent, as illustrated in FIG. 27. However, the median value ofh_(τ)*(x−y) would be more robust when the narrow-band signal of interestis affected by short-duration outliers such as broadband impulsivenoise, since such outliers would not be excessively broadened by thewide-band filter h_(τ)(t). In addition, while being wide-band, thisfilter would prevent the amplitude of the background noise observed atthe input of the blanker from being excessively large.

With τ given by equation (31), the parameter γ may be chosen as

$\begin{matrix}{{\gamma \approx \frac{1}{4\pi \; B_{x}\tau} \approx {\frac{1}{2}\sqrt{\frac{F_{s}}{B_{x}}}}},} & (34)\end{matrix}$

and the relation between the input and the output of the ΔΣ ADCs with aCMTF-based loop filter may be expressed as

x(t−Δt)≈((w+γτ{dot over (w)})*y)(t).  (35)

Note that for large blanking values such that α≥|h_(τ)*(x−y) for all t,according to equation (33) the average rate of change of h_(τ)*y wouldbe proportional to the average of the difference signal h_(τ)*(x−y).When the magnitude of the difference signal h_(τ)*(x−y) exceeds theblanking value α, however, the average rate of change of h_(τ)*y wouldbe zero and would no longer depend on the magnitude of h_(τ)*x,providing an output that would be insensitive to outliers with acharacteristic amplitude determined by the blanking value α.

Since linear filters are generally better than median for removingbroadband Gaussian (e.g. thermal) noise, the blanking value in theCMTF-based topology should be chosen to ensure that the CMTF-based ΔΣADC performs effectively linearly when outliers are not present, andthat it exhibits nonlinear behavior only intermittently, in response tooutlier noise. An example of a robust approach to establishing such ablanking value is outlined in § 5.2.

One skilled in the art will recognize that the ΔΣ modulator depicted inFIG. 26 comprises a quantizer (flip-flop), a blanker, two integrators,and two wide-bandwidth 1st order lowpass filters, and the (nonlinear)loop filter of this modulator is configured in such a way that the valueof the quantized representation (signal y(t)) of the input signal x(t),averaged over a time interval ΔT comparable with an inverse of thenominal bandwidth of the signal of interest, is effectively proportionalto a nonlinear measure of central tendency of said input signal x(t) insaid time interval ΔT.

5.1 Simplified Performance Example

Let us first use a simplified synthetic signal to illustrate theessential features, and the advantages provided by the ΔΣ ADC with theCMTF-based loop filter configuration when the impulsive noise affectingthe signal of interest dominates over a low-level background Gaussiannoise.

In this example, the signal of interest consists of two fragments of twosinusoidal tones with 0.9V amplitudes, and with frequencies B_(x) andB_(x)/8, respectively, separated by zero-value segments. While pure sinewaves are chosen for an ease of visual assessment of the effects of thenoise, one may envision that the low-frequency tone corresponds to avowel in a speech signal, and that the high-frequency tone correspondsto a fricative consonant.

For all ΔΣ ADCs in this illustration, the flip-flop clock frequency isF_(s)=NB_(x), where N=1024. For the 2nd-order loop filter in thisillustration τ=(4πB_(x))⁻¹. The time constant τ of the 1st order lowpassfilters in the CMTF-based loop filter is τ=(2πB_(x)√{square root over(N)})⁻¹=(64πB_(x))⁻¹, and γ=16 (resulting in γτ=(4πB_(x))⁻¹). Theparameter α is chosen as α=V_(c). The output y[k] of the ΔΣ ADC with the1st-order linear loop filter (panel I of FIG. 1) is filtered with adigital lowpass filter with the impulse response w[k]. The outputs ofthe ΔΣ ADCs with the 2nd-order linear (panel II of FIG. 1) and theCMTF-based (FIG. 5) loop filters are filtered with a digital lowpassfilter with the impulse response w[k]+(4πB_(x))⁻¹{dot over (w)}[k]. Theimpulse and frequency responses of w[k] and w[k]+(4πB_(x))⁻¹{dot over(w)}[k] are shown in FIG. 28.

As shown in panel I of FIG. 29, the signal is affected by a mixture ofadditive white Gaussian noise (AWGN) and white impulse (outlier) noisecomponents, both band-limited to approximately B_(x)√{square root over(N)} bandwidth. As shown in panel II, in the absence of the outliernoise, the performance of all ΔΣ ADC in this example is effectivelyequivalent, and the amount of the AWGN is such that the resultingsignal-to-noise ratio for the filtered output is approximately 20 dB inthe absence of the outlier noise. The amount of the outlier noise issuch that the resulting signal-to-noise ratio for the filtered output ofthe ΔΣ ADC with a 1st-order linear loop filter is approximately 6 dB inthe absence of the AWGN.

As one may see in panels III and IV of FIG. 29, the linear loop filtersare ineffective in suppressing the impulsive noise. Further, theperformance of the ΔΣ ADC with the 2nd-order linear loop filter (seepanel IV of FIG. 29) is more severely degraded by high-power noise,especially by high-amplitude outlier noise such that the condition|x(t−Δt)+(w*v)(t)|<V_(c) is not satisfied for all t. On the other hand,as may be seen in panel V of FIG. 29, the ΔΣ ADC with the CMTF-basedloop filter improves the signal-to-noise ratio by about 13 dB incomparison with the ΔΣ ADC with the 1st-order linear loop filter, thusremoving about 95% of the impulsive noise.

More importantly, as may be seen in panel III of FIG. 30, increasing theimpulsive noise power by an order of magnitude hardly affects the outputof the ΔΣ ADC with the CMTF-based loop filter (and thus about 99.5% ofthe impulsive noise is removed), while further exceedingly degrading theoutput of the ΔΣ ADC with the 1st-order linear loop filter (panel II).

5.2 ΔΣ ADC with Adaptive CMTF

A CMTF with an adaptive (possibly asymmetric) blanking range [a⁻, ac]may be designed as follows. To ensure that the values of the differencesignal h_(T)*(x−y) that lie outside of [α⁻, α₊] are outliers, one mayidentify [a⁻, α₊] with Tukey's range [46], a linear combination of the1st (Q₁) and the 3rd (Q₃) quartiles of the difference signal (see [33,34] for discussion of quantiles of continuous signals):

[α⁻,α₊ ]=[Q ₁−β(Q ₃ −Q ₁),Q ₃+β(Q ₃ −Q ₁)],  (36)

where β is a coefficient of order unity (e.g. β=1.5). From equation(36), for a symmetrical distribution the range that excludes outliersmay also be obtained as [α⁻, α₊]=[−α, α], where α is given by

α=(1+2β)Q* ₂,  (37)

and where Q*₂ is the 2nd quartile (median) of the absolute value (ormodulus) of the difference signal |h_(τ)*(x−y)|.

Alternatively, since 2Q*₂=Q₃−Q₁ for a symmetrical distribution, theresolution parameter α may be obtained as

α=(½+β)(Q ₃ −Q ₁),  (38)

where Q₃−Q₁ is the interquartile range (IQR) of the difference signal.

FIG. 31 provides an outline of a ΔΣ ADC with an adaptive CMTF-based loopfilter. In this example, the 1st order lowpass filters are followed bythe gain stages with the gain G, while the blanking value is set toV_(c). Note that

$\begin{matrix}{{{\mathcal{B}_{V_{c}}({Gx})} = {G\; {\mathcal{B}_{\frac{V_{c}}{G}}(x)}}},} & (39)\end{matrix}$

and thus the “apparent” (or “equivalent”) blanking value would be nolonger hardware limited. As shown in FIG. 31, the input x(t) and theoutput y(t) may be related by

$\begin{matrix}{{\frac{d}{dt}\overset{\_}{h_{\tau}*y}} = {\frac{1}{\gamma\tau}{\overset{\_}{\mathcal{B}_{\frac{V_{c}}{G}}\left( {h_{\tau}*\left( {x - y} \right)} \right)}.}}} & (40)\end{matrix}$

If an automatic gain control circuit maintains a constant output−V_(c)/(1+2β) of the MTF circuit in FIG. 31, then the apparent blankingvalue α=V_(c)/G in equation (40) may be given by equation (37).

5.2.1 Performance Example

Simulation Parameters—

To emulate the analog signals in the examples below, the digitizationrate is two orders of magnitude higher than the sampling rate F_(s). Thesignal of interest is a Gaussian baseband signal in the nominalfrequency rage [0, B_(x)]. It is generated as a broadband white Gaussiannoise filtered with a root-raised-cosine filter with the roll-off factor¼ and the bandwidth 5B_(x)/4. The noise affecting the signal of interestis a sum of an AWGN background component and white impulsive noise i(t).The impulsive noise is modeled as symmetrical (bipolar) Poisson shotnoise:

$\begin{matrix}{{{i(t)} = {{v(t)}{\sum\limits_{k = 1}^{\infty}\; {\delta \left( {t - t_{k}} \right)}}}},} & (41)\end{matrix}$

where v(t) is AWGN noise, t_(k) is the k-th arrival time of a Poissonprocess with the rate parameter Δ, and δ(x) is the Dirac δ-function[31]. In the examples below, λ=B_(x). The gain C is chosen to maintainthe output of the MTF in FIG. 31 at −V_(c)/(1+2β), and the digitallowpass filter w[k] is the root-raised-cosine filter with the roll-offfactor ¼ and the bandwidth 5B_(x)/4. The remaining hardware parametersare the same as those in § 5.1. Further, the magnitude of the input x(t)is chosen to ensure that the average absolute value of the output signalis approximately V_(c)/5.

Comparative Channel Capacities—

For the simulation parameters described above, FIG. 32 compares thesimulated channel capacities (calculated from the baseband SNRs usingthe Shannon formula [42]) for various signal+noise compositions, for thelinear signal processing chain (solid lines) and the CMTF-based chain ofFIG. 31 with β=1.5 (dotted lines).

As one may see in FIG. 32 (and compare with the simplified diagram ofFIG. 2), linear and the CMTF-based chains provide effectively equivalentperformance when the AWGN dominates over the impulsive noise. However,the CMTF-based chains are insensitive to further increase in theimpulsive noise when the latter becomes comparable or dominates over thethermal (Gaussian) noise, thus providing resistance to impulsiveinterference.

Disproportionate Effect on Baseband PSDs—

For a mixture of white Gaussian and white impulsive noise, FIG. 33Aillustrates reduction of the spectral density of impulsive noise in thesignal baseband without affecting that of the signal of interest. In thefigure, the solid lines correspond to the “ideal” signal of interest(without noise), and the dotted lines correspond to the signal+noisemixtures. The baseband power of the AWGN is one tenth of that of thesignal of interest (10 dB AWGN SNR), and the baseband power of theimpulsive noise is approximately 8 times (9 dB) that of the AWGN. Thevalue of the parameter β for Tukey's range is β=1.5. As may be seen inthe figure, for the CMTF-based chain the baseband SNR increases from 0.5dB to 9.7 dB.

For both the linear and the CMTF-based chains the observed basebandnoise may be considered to be effectively Gaussian, and we may use theShannon formula [42] based on the achieved baseband SNRs to calculatethe channel capacities. Those are marked by the asterisks on therespective solid and dotted curves in FIG. 32.

FIG. 33B provides a similar illustration with additional interference inan adjacent channel. Such interference increases the apparent blankingvalue needed to maintain effectively linear CMTF behavior in the absenceof the outliers, slightly reducing the effectiveness of the impulsivenoise suppression. As a result, the baseband SNR increases from 0.5 dBto only 8.5 dB.

6 ΔΣ ADCs with Linear Loop Filters and Digital ADiC/CMTF Filtering

While § 5 describes CMTF-based outlier noise filtering of the analoginput signal incorporated into loop filters of ΔΣ analog-to-digitalconverters, the high raw sampling rate (e.g. the flip-flop clockfrequency) of a ΔΣ ADC (e.g. two to three orders of magnitude largerthan the bandwidth of the signal of interest) may be used for effectiveABAINF/CMTF/ADiC-based outlier filtering in the digital domain,following a ΔΣ modulator with a linear loop filter.

FIG. 34 shows illustrative signal chains for a ΔΣ ADC with linear loopand decimation filters (panel (a)), and for a ΔΣ ADC with linear loopfilter and ADiC-based digital filtering (panel (b)). As may be seen inpanel (a) of FIG. 34, the quantizer output of a ΔΣ ADC with linear loopfilter would be filtered with a linear decimation filter that wouldtypically combine lowpass filtering with downsampling. To enable anADiC-based outlier filtering (panel (b)), a wideband (e.g. withbandwidth approximately equal to the geometric mean of the nominalsignal bandwidth B_(x) and the sampling frequency F_(s)) digital filteris first applied to the output of the quantizer. The output of thisfilter is then filtered by a digital ADiC (with appropriately chosentime parameter and the blanking range), followed by a linearlowpass/decimation filter.

FIG. 35 shows illustrative time-domain traces at points I through VI ofFIG. 34, and the output of the ΔΣ ADC with linear loop and decimationfilters for the signal affected by AWGN only (w/o impulsive noise). Inthis example, a 1st order ΔΣ modulator is used, and the quantizerproduces a 1-bit output shown in panel II. The digital wideband filteris a 2nd order IIR Bessel filter with the corner frequency approximatelyequal to the geometric mean of the nominal signal bandwidth B_(x) andthe sampling frequency F_(s). The time parameter of the ADiC isapproximately τ≈(4πB_(x))⁻¹, and the same lowpass/decimation filter isused as for the linear chain of FIG. 34 (a).

FIG. 36 shows illustrative signal chains for a ΔΣ ADC with linear loopand decimation filters (panel (a)), and for a ΔΣ ADC with linear loopfilter and CMTF-based digital filtering (panel (b)). To enable aCMTF-based outlier filtering (panel (b)), a wideband digital filter isfirst applied to the output of the quantizer. The output of this filteris then filtered by a digital CMTF (with the time constant τ andappropriately chosen blanking range), followed by a linear lowpassfiltering (with the modified impulse response w[k]+τ{dot over (w)}[k])combined with decimation.

FIG. 37 shows illustrative time-domain traces at points I through VI ofFIG. 36, and the output of the ΔΣ ADC with linear loop and decimationfilters for the signal affected by AWGN only (w/o impulsive noise). Inthis example, a 1st order ΔΣ modulator is used, and the quantizerproduces a 1-bit output shown in panel II. The digital wideband filteris a 2nd order IIR Bessel filter with the corner frequency approximatelyequal to the geometric mean of the nominal signal bandwidth B and thesampling frequency F_(s). The time parameter of the CMTF isτ=(4πB_(x))⁻¹, and the impulse response of the lowpass filter in thedecimation stage is modified as w[k]+(4τB_(x))⁻¹ {dot over (w)}[k].

To prevent excessive distortions of the quantizer output byhigh-amplitude transients (especially for high-order ΔΣ modulators), andthus to increase the dynamic range of the ADC and/or the effectivenessof outlier filtering, an analog clipper (with appropriately chosenclipping values) should precede the ΔΣ modulator, as schematically shownin FIGS. 38 and 40.

FIG. 38 shows illustrative signal chains for a ΔΣ ADC with linear loopand decimation filters (panel (a)), and for a ΔΣ ADC with linear loopfilter and ADiC-based digital filtering (panel (b)), with additionalclipping of the analog input signal.

FIG. 39 shows illustrative time-domain traces at points I through VI ofFIG. 38, and the output of the ΔΣ ADC with linear loop and decimationfilters for the signal affected by AWGN only (w/o impulsive noise). Inthis example, a 1st order ΔΣ modulator is used, and the quantizerproduces a 1-bit output. The digital wideband filter is a 2nd order IIRBessel filter with the corner frequency approximately equal to thegeometric mean of the nominal signal bandwidth B_(x) and the samplingfrequency F_(s). The time parameter of the ADiC is approximatelyτ≈(4πB_(x))⁻¹, and the same lowpass/decimation filter is used as for thelinear chain of FIG. 38 (a).

FIG. 40 shows illustrative signal chains for a ΔΣ ADC with linear loopand decimation filters (panel (a)), and for a ΔΣ ADC with linear loopfilter and CMTF-based digital filtering (panel (b)), with additionalclipping of the analog input signal.

FIG. 41 shows illustrative time-domain traces at points I through VI ofFIG. 40, and the output of the ΔΣ ADC with linear loop and decimationfilters for the signal affected by AWGN only (w/o impulsive noise). Inthis example, a 1st order ΔΣ modulator is used, and the quantizerproduces a 1-bit output. The digital wideband filter is a 2nd order IIRBessel filter with the corner frequency approximately equal to thegeometric mean of the nominal signal bandwidth B_(x) and the samplingfrequency F_(s). The time parameter of the CMTF is τ=(4πB_(x))⁻¹, andthe impulse response of the lowpass filter in the decimation stage ismodified as w[k]+(4πB_(x))⁻¹{dot over (w)}[k].

7 Additional Comments

It should be understood that the specific examples in this disclosure,while indicating preferred embodiments of the invention, are presentedfor illustration only. Various changes and modifications within thespirit and scope of the invention should become apparent to thoseskilled in the art from this detailed description. Furthermore, all themathematical expressions, diagrams, and the examples of hardwareimplementations are used only as a descriptive language to convey theinventive ideas clearly, and are not limitative of the claimedinvention.

Further, one skilled in the art will recognize that the variousequalities and/or mathematical functions used in this disclosure areapproximations that are based on some simplifying assumptions and areused to represent quantities with only finite precision. We may use theword “effectively” (as opposed to “precisely”) to emphasize that only afinite order of approximation (in amplitude as well as time and/orfrequency domains) may be expected in hardware implementation.

Ideal Vs. “Real” Blankers—

For example, we may say that an output of a blanker characterized by ablanking value is effectively zero when the absolute value (modulus) ofsaid output is much smaller (e.g. by an order of magnitude or more) thanthe blanking range.

In addition to finite precision, a “real” blanker may be characterizedby various other non-idealities. For example, it may exhibit hysteresis,when the blanker's state depends on its history.

For a “real” blanker, when the value of its input x extends outside ofits blanking range [α⁻, α₊], the value of its transparancy functionwould decrease to effectively zero value over some finite range of theincrease (decrease) in x. If said range of the increase (decrease) in xis much smaller (e.g. by an order of magnitude or more) than theblanking range, we may consider such a “real” blanker as beingeffectively described by equations (15), (27) and/or (32).

Further, in a “real” blanker the change in the blanker's output may be“lagging”, due to various delays in a physical circuit, the change inthe input signal. However, when the magnitude of such lagging issufficiently small (e.g. smaller than the inverse bandwidth of the inputsignal), and provided that the absolute value of the blanker outputdecreases to effectively zero value, or restores back to the inputvalue, over a range of change in x much smaller than the blanking range(e.g. by an order of magnitude or more), we may consider such a “real”blanker as being effectively described by equations (15), (27) and/or(32).

7.1 Mitigation of Non-Gaussian (e.g. Outlier) Noise in the Process ofAnalog-to-Digital Conversion: Analog and Digital Approaches

Conceptually, ABAINFs are analog filters that combine bandwidthreduction with mitigation of interference. One may think of non-Gaussianinterference as having some temporal and/or amplitude structure thatdistinguishes it form a purely random Gaussian (e.g. thermal) noise.Such structure may be viewed as some “coupling” among differentfrequencies of a non-Gaussian signal, and may typically require arelatively wide bandwidth to be observed. A linear filter thatsuppresses the frequency components outside of its passband, whilereducing the non-Gaussian signal's bandwidth, may destroy this coupling,altering the structure of the signal. That may complicate furtheridentification of the non-Gaussian interference and its separation froma Gaussian noise and the signal of interest by nonlinear filters such asABAINFs.

In order to mitigate non-Gaussian interference efficiently, the inputsignal to an ABAINF would need to include the noise and interference ina relatively wide band, much wider (e.g. ten times wider) than thebandwidth of the signal of interest. Thus the best conceptual placementfor an ABAINF may be in the analog part of the signal chain, forexample, ahead of an ADC, or incorporated into the analog loop filter ofa ΔΣ ADC. However, digital ABAINF implementations may offer manyadvantages typically associated with digital processing, including, butnot limited to, simplified development and testing, configurability, andreproducibility.

In addition, as illustrated in § 3.3, a means of tracking the range ofthe difference signal that effectively excludes outliers of thedifference signal may be easily incorporated into digital ABAINFimplementations, without a need for separate circuits implementing sucha means.

While real-time finite-difference implementations of the ABAINFsdescribed above would be relatively simple and computationallyinexpensive, their efficient use would still require a digital signalwith a sampling rate much higher (for example, ten times or more higher)than the Nyquist rate of the signal of interest.

Since the magnitude of a noise affecting the signal of interest wouldtypically increase with the increase in the bandwidth, while theamplitude of the signal+noise mixture would need to remain within theADC range, a high-rate sampling may have a perceived disadvantage oflowering the effective ADC resolution with respect to the signal ofinterest, especially for strong noise and/or weak signal of interest,and especially for impulsive noise. However, since the sampling ratewould be much higher (for example, ten times or more higher) than theNyquist rate of the signal of interest, the ABAINF output may be furtherfiltered and downsampled using an appropriate decimation filter (forexample, a polyphase filter) to provide the desired higher-resolutionsignal at lower sampling rate. Such a decimation filter may counteractthe apparent resolution loss, and may further increase the resolution(for example, if the ADC is based on ΔΣ modulators).

Further, a simple (non-differential) “hard” or “soft.” clipper may beemployed ahead of an ADC to limit the magnitude of excessively strongoutliers in the input signal.

As discussed earlier, mitigation of non-Gaussian (e.g. outlier) noise inthe process of analog-to-digital conversion may be achieved by deployinganalog ABAINFs (e.g. CMTFs or ADiCs) ahead of the anti-aliasing filterof an ADC, or by incorporating them into the analog loop filter of a ΔΣADC, as illustrated in FIGS. 42(a) and 43(a), respectively.

Alternatively, as illustrated in FIG. 42(b), a wider-bandwidthanti-aliasing filter may be employed ahead of an ADC, and an ADC with arespectively higher sampling rate may be employed in the digital part. Adigital ABAINF (e.g. CMTF or ADiC) may then be used to reducenon-Gaussian (e.g. impulsive) interference affecting a narrower-bandsignal of interest. Then the output of the ABAINF may be furtherfiltered with a digital filter, (optionally) downsampled, and passed tothe subsequent digital signal processing.

Prohibitively low (e.g. 1-bit) amplitude resolution of the output of aΔΣ modulator would not allow direct application of a digital ABAINF.However, since the oversampling rate of a ΔΣ modulator would besignificantly higher (e.g. by two to three orders of magnitude) than theNyquist rate of the signal of interest, a wideband (e.g. with bandwidthapproximately equal to the geometric mean of the nominal signalbandwidth B₇ and the sampling frequency F_(s)) digital filter may befirst applied to the output of the quantizer to enable ABAINF-basedoutlier filtering, as illustrated in FIG. 43(b).

It may be important to note that the output of such a wideband digitalfilter would still contain a significant amount of high-frequencydigitization (quantization) noise. As follows from the discussion in §3, the presence of such noise may significantly simplify using quantiletracking filters as a means of determining the range of the differencesignal that effectively excludes outliers of the difference signal.

The output of the wideband filter may then be filtered by a digitalABAINF (with appropriately chosen time parameter and the blankingrange), followed by a linear lowpass/decimation filter.

7.2 Comments on ΔΣ Modulators

The 1st order ΔΣ modulator shown in panel I of FIG. 1 may be describedas follows. The input D to the flip-flop, or latch, is proportional toan integrated difference between the input signal x(t) of the modulatorand the output Q. The clock input to the flip-flop provides a controlsignal. If the input D to the flip-flop is greater than zero,D>0, at, adefinite portion of the clock cycle (such as the rising edge of theclock), then the output Q takes a positive value V_(c), Q=V_(c). If D<0at a rising edge of the clock, then the output Q takes a negative value−V_(c), Q=−V_(c). At other times, the output Q does not change. It maybe assumed that Q is the compliment of Q and Q=−Q.

Without loss of generality, we may require that if D=0 at a clock'srising edge, the output Q retains its previous value.

One may see in panel I of FIG. 1 that the output Q is a quantizedrepresentation of the input signal, and the flip-flop may be viewed as aquantizer. One may also see that the integrated difference between theinput signal of the modulator and the output Q (the input D to theflip-flop) may be viewed as a particular type of a weighted differencebetween the input and the output signals. One may further see that theoutput Q is indicative of this weighted difference, since the sign ofthe output values (positive or negative) is determined by the sign ofthe weighted difference (the input D to the flip-flop).

One skilled in the art will recognize that the digital quantizer in a ΔΣmodulator may be replaced by its analog “equivalent” (i.e. Schmitttrigger, or comparator with hysteresis).

Also, the quantizer may be realized with an N-level comparator, thus themodulator would have a log₂(N)-bit output. A simple comparator with 2levels would be a 1-bit quantizer; a 3-level quantizer may be called a“1.5-bit” quantizer; a 4-level quantizer would be a 2-bit quantizer; a5-level quantizer would be a “2.5-bit” quantizer.

7.3 Comparators, Discriminators, Clippers, and Limiters

A comparator, or a discriminator, may be typically understood as acircuit or a device that only produces an output when the input exceedsa fixed value.

For example, consider a simple measurement process whereby a signal x(t)is compared to a threshold value D. The ideal measuring device wouldreturn ‘0’ or ‘1’ depending on whether x(t) is larger or smaller than D.The output of such a device may be represented by the Heaviside unitstep function θ (D−x(t)) [30], which is discontinuous at zero. Such adevice may be called an ideal comparator, or an ideal discriminator.

More generally, a discriminator/comparator may be represented by acontinuous discriminator function

_(α)(x) with a characteristic width (resolution) a such that lim_(α→0)

_(α)(x)=θ(x).

In practice, many different circuits may serve as discriminators, sinceany continuous monotonic function with constant unequal horizontalasymptotes would produce the desired response under appropriate scalingand reflection. For example, the voltage-current characteristic of asubthreshold transconductance amplifier [49, 50] may be described by thehyperbolic tangent function,

_(α)(x)=A tan h(x/α). Note that

${{\lim_{\alpha\rightarrow 0}\frac{{{\overset{\sim}{\mathcal{F}}}_{\alpha}(x)} - A}{2A}} = {\theta (x)}},$

and thus such an amplifier may serve as a discriminator.

When α<<A, a continuous comparator may be called a high-resolutioncomparator.

A particularly simple continuous discriminator function with a “ramp”transition may be defined as

$\begin{matrix}{{\mathcal{F}_{g,A}(x)} = \left\{ {\begin{matrix}{gx} & \left. {{for}\mspace{14mu} g} \middle| x \middle| {\leq A} \right. \\{A\mspace{14mu} {{sgn}(x)}} & {otherwise}\end{matrix},} \right.} & (42)\end{matrix}$

where g may be called the gain of the comparator, and A is thecomparator limit.

Note that a high-gain comparator would be a high-resolution comparator.

The “ramp” comparator described by equation (42) may also be called aclipping amplifier (or simply a “clipper”) with the clipping value A andgain g.

For asymmetrical clipping values α₊ (upper) and a⁻ (lower), a clippermay be described by the following clipping function C_(α−) ^(α+)(x):

$\begin{matrix}{{_{\alpha_{-}}^{\alpha_{+}}(x)} = \left\{ {\begin{matrix}\alpha_{+} & {{{for}\mspace{14mu} x} > \alpha_{+}} \\\alpha_{-} & {{{for}\mspace{14mu} x} < \alpha_{-}} \\x & {otherwise}\end{matrix}.} \right.} & (43)\end{matrix}$

It may be assumed in this disclosure that the outputs of the activecomponents (such as, e.g., the active filters, integrators, and thegain/amplifier stages) may be limited to (or clipped at) certain finiteranges, for example, those determined by the power supplies, and thatthe recovery times from such saturation may be effectively negligible.

7.4 Nonlinear Measures of Central Tendency

A measure of central tendency would be a single value that attempts todescribe a set, of data by identifying the central position within thatset of data. As such, measures of central tendency are sometimes calledmeasures of central location. They are also may be classed as summarystatistics. The mean (often called the average), or weighted mean(weighted average) would be the most typically used measure of centraltendency, and, when the weights do not depend on the data values, it maybe considered a linear measure of central tendency.

An example of a (generally) nonlinear measure of central tendency wouldbe the quasiarithmetic mean or generalized ƒ-mean [51].

Other nonlinear measures of central tendency may include such measuresas a median or a truncated mean value, or an L-estimator [46, 52, 53].

One skilled in the art will recognize that an output of a CMTF may beconsidered to be a nonlinear measure of central tendency of its input.

7.5 Mitigation of Non-Impulsive Non-Gaussian Noise

The temporal and/or amplitude structure (and thus the distributions) ofnon-Gaussian signals are generally modifiable by linear filtering, andnon-Gaussian interference may often be converted from sub-Gaussian intosuper-Gaussian, and vice versa, by linear filtering [9, 10, 32, e.g.].Thus the ability of the ADiCs/CMTFs disclosed herein, and ΔΣ ADCs withanalog nonlinear loop filters, to mitigate impulsive (super-Gaussian)noise may translate into mitigation of non-Gaussian noise andinterference in general, including sub-Gaussian noise (e.g. wind noiseat microphones). For example, a linear analog filter may be employed asan input front end filter of the ADC to increase the peakedness of theinterference, and the ΔΣ ADCs with analog nonlinear loop filter mayperform analog-to-digital conversion combined with mitigation of thisinterference. Subsequently, if needed, a digital filter may be employedto compensate for the impact of the front end filter on the signal ofinterest.

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Regarding the invention being thus described, it will be obvious thatthe same may be varied in many ways. Such variations are not to beregarded as a departure from the spirit and scope of the invention, andall such modifications as would be obvious to one skilled in the art areintended to be included within the scope of the claims. It is to beunderstood that while certain now preferred forms of this invention havebeen illustrated and described, it is not limited thereto except insofaras such limitations are included in the following claims.

I claim:
 1. An apparatus for signal filtering capable of converting aninput signal into an output signal, wherein said input signal is aphysical signal and wherein said output signal is a physical signal, theapparatus comprising: a) a blanker characterized by a blanking range andoperable to receive a blanker input and to produce a blanker output,wherein said blanker output is proportional to said blanker input whensaid blanker input is within said blanking range, and wherein saidblanker output is effectively zero when said blanker input is outside ofsaid blanking range; b) an integrator characterized by an integrationtime constant and operable to receive an integrator input and to producean integrator output, wherein said integrator output is proportional toan antiderivative of said integrator input; wherein said blanker inputis proportional to a difference signal, wherein said difference signalis the difference between said input signal and said output signal,wherein said integrator input is proportional to said blanker output,and wherein said output signal is proportional to said integratoroutput.
 2. The apparatus of claim 1 wherein said blanking range is arange that effectively excludes outliers of said blanker input.
 3. Theapparatus of claim 1 further comprising a means of establishing saidblanking range, wherein said means comprises a quantile tracking filteroperable to receive said blanker input and to produce a quantiletracking filter output.
 4. The apparatus of claim 1 further comprising ameans of establishing said blanking range, wherein said means comprisesa quantile tracking filter operable to receive an input proportional toan absolute value of said blanker input and to produce a quantiletracking filter output.
 5. The apparatus of claim 1 further comprising ameans of establishing said blanking range, wherein said means comprisesa plurality of quantile tracking filters operable to receive saidblanker input and to produce a plurality of quantile tracking filteroutputs, and wherein said blanking range is a linear combination of saidplurality of quantile tracking filter outputs.
 6. An apparatus forsignal filtering capable of converting an input signal into an outputsignal, wherein said input signal is a physical signal and wherein saidoutput signal is a physical signal, the apparatus comprising: a) ablanker characterized by a blanking range and operable to receive ablanker input and to produce a blanker output, wherein said blankeroutput is proportional to said blanker input when said blanker input iswithin said blanking range, and wherein said blanker output iseffectively zero when said blanker input is outside of said blankingrange; b) an integrator characterized by an integration time constantand operable to receive an integrator input and to produce an integratoroutput, wherein said integrator output is proportional to anantiderivative of said integrator input; wherein said blanker input isproportional to a difference signal, wherein said difference signal isthe difference between said input signal and said output signal, whereinsaid integrator input is proportional to said blanker output, andwherein said output signal is proportional to a sum of said integratorinput and said integrator output.
 7. The apparatus of claim 6 whereinsaid blanking range is a range that effectively excludes outliers ofsaid blanker input.
 8. The apparatus of claim 6 further comprising ameans of establishing said blanking range, wherein said means comprisesa quantile tracking filter operable to receive said blanker input and toproduce a quantile tracking filter output.
 9. The apparatus of claim 6further comprising a means of establishing said blanking range, whereinsaid means comprises a quantile tracking filter operable to receive aninput proportional to an absolute value of said blanker input and toproduce a quantile tracking filter output.
 10. The apparatus of claim 6further comprising a means of establishing said blanking range, whereinsaid means comprises a plurality of quantile tracking filters operableto receive said blanker input and to produce a plurality of quantiletracking filter outputs, and wherein said blanking range is a linearcombination of said plurality of quantile tracking filter outputs. 11.An apparatus for analog-to-digital conversion capable of converting aninput signal into an output signal, wherein said input signal is aphysical signal characterized by a nominal bandwidth and wherein saidoutput signal is a quantized representation of said input signal, theapparatus comprising: a) a quantizer operable to receive a quantizerinput and to produce a quantizer output; b) a nonlinear loop filteroperable to receive said input signal and a feedback of said quantizeroutput and to produce said quantizer input, said nonlinear loop filterfurther comprising: c) a blanker characterized by a blanking range andoperable to receive a blanker input and to produce a blanker output,wherein said blanker output is proportional to said blanker input whensaid blanker input is within said blanking range, and wherein saidblanker output is effectively zero when said blanker input is outside ofsaid blanking range; d) a first integrator characterized by a firstintegration time constant and operable to receive a first integratorinput and to produce a first integrator output, wherein said firstintegrator output is proportional to an antiderivative of said firstintegrator input; e) a second integrator characterized by a secondintegration time constant and operable to receive a second integratorinput and to produce a second integrator output, wherein said secondintegrator output is proportional to an antiderivative of said secondintegrator input; f) a first 1st order lowpass filter characterized by alowpass filter bandwidth and a second 1st order lowpass filtercharacterized by said lowpass filter bandwidth, wherein said lowpassfilter bandwidth is much larger than said nominal bandwidth, whereinsaid first 1st order lowpass filter is operable to receive a first 1storder lowpass filter input and to produce a first 1st order lowpassfilter output, and wherein said second 1st order lowpass filter isoperable to receive a second 1st order lowpass filter input and toproduce a second 1st order lowpass filter output; wherein said first 1storder lowpass filter input is proportional to a difference between saidinput signal and said feedback of said quantizer output, wherein saidsecond 1st order lowpass filter input is proportional to said feedbackof said quantizer output, wherein said blanker input is proportional tosaid first 1st order lowpass filter output, wherein said firstintegrator input is proportional to said blanker output, wherein saidsecond integrator input is proportional to a difference between saidsecond integrator output and said second 1st order lowpass filteroutput, and wherein said quantizer input is proportional to said secondintegrator output.
 12. The apparatus of claim 11 wherein said blankingrange is a range that effectively excludes outliers of said blankerinput.
 13. The apparatus of claim 11 further comprising a means ofestablishing said blanking range, wherein said means comprises aquantile tracking filter operable to receive said blanker input and toproduce a quantile tracking filter output.
 14. The apparatus of claim 11further comprising a means of establishing said blanking range, whereinsaid means comprises a quantile tracking filter operable to receive aninput proportional to an absolute value of said blanker input and toproduce a quantile tracking filter output.
 15. The apparatus of claim 11further comprising a means of establishing said blanking range, whereinsaid means comprises a plurality of quantile tracking filters operableto receive said blanker input and to produce a plurality of quantiletracking filter outputs, and wherein said blanking range is a linearcombination of said plurality of quantile tracking filter outputs. 16.The apparatus of claim 11 wherein said first 1st order lowpass filter isfurther characterized by a gain value and wherein said second 1st orderlowpass filter is further characterized by said gain value.
 17. Theapparatus of claim 16 further comprising a means of establishing gainvalue, wherein said means comprises a quantile tracking filter operableto receive an input proportional to an absolute value of said blankerinput and to produce a quantile tracking filter output.
 18. A digitalsignal processing apparatus comprising a digital signal processing unitconfigurable to perform one or more functions including a filteringfunction transforming an input signal into an output filtered signal,wherein said filtering function comprises: a) a blanker functioncharacterized by a blanking range and operable to receive a blankerinput and to produce a blanker output, wherein said blanker output isproportional to said blanker input when said blanker input is withinsaid blanking range, and wherein said blanker output is effectively zerowhen said blanker input is outside of said blanking range; b) anintegrator function characterized by an integration time constant andoperable to receive an integrator input and to produce an integratoroutput, wherein said integrator output is proportional to a numericalantiderivative of said integrator input; wherein said blanker input isproportional to a difference signal, wherein said difference signal isthe difference between said input signal and said output signal, whereinsaid integrator input is proportional to said blanker output, andwherein said output filtered signal is proportional to said integratoroutput.
 19. The apparatus of claim 18 wherein said blanking range is arange that effectively excludes outliers of said blanker input.
 20. Theapparatus of claim 18 further comprising a means of estimating saidblanking range, wherein said means comprises a quantile trackingfunction estimating a quantile of said blanker input.
 21. The apparatusof claim 18 further comprising a means of estimating said blankingrange, wherein said means comprises a quantile tracking functionestimating a quantile of an absolute value of said blanker input. 22.The apparatus of claim 18 further comprising a means of estimating saidblanking range, wherein said means comprises a plurality of quantiletracking functions, wherein said plurality of quantile trackingfunctions estimates a plurality of quantiles of said blanker input, andwherein said blanking range is a linear combination of said plurality ofquantiles.